1
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Yalovetzky R, Minssen P, Herman D, Pistoia M. Solving linear systems on quantum hardware with hybrid HHL +. Sci Rep 2024; 14:20610. [PMID: 39256450 PMCID: PMC11387654 DOI: 10.1038/s41598-024-69077-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2024] [Accepted: 07/31/2024] [Indexed: 09/12/2024] Open
Abstract
The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using useful quantum algorithms, i.e., application-oriented benchmarking. In particular, the Harrow-Hassidim-Lloyd (HHL) algorithm is a critical quantum linear algebra primitive, but the majority of the components of HHL are far out of the reach of noisy intermediate-scale quantum devices, which has led to the proposal of hybrid classical-quantum variants. The goal of this work is to further bridge the gap between proposed near-term friendly implementations of HHL and the kinds of quantum circuits that can be executed on noisy hardware. Our proposal adds to the existing literature of hybrid quantum algorithms for linear algebra that are more compatible with the current scale of quantum devices. Specifically, we propose two modifications to the Hybrid HHL algorithm proposed by Lee et al., leading to our algorithm Hybrid HHL + + : (1) propose a novel algorithm for determining a scaling factor for the linear system matrix that maximizes the utility of the amount of ancillary qubits allocated to the phase estimation component of HHL, and (2) introduce a heuristic for compressing the HHL circuit. We demonstrate the efficacy of our work by running our modified Hybrid HHL on Quantinuum System Model H-series trapped-ion quantum computers to solve different problem instances of small-scale portfolio optimization problems, leading to the largest experimental demonstrations of HHL for an application to date.
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Affiliation(s)
- Romina Yalovetzky
- Global Technology Applied Research, JPMorganChase, New York, NY, 10017, USA.
| | - Pierre Minssen
- Global Technology Applied Research, JPMorganChase, New York, NY, 10017, USA
| | - Dylan Herman
- Global Technology Applied Research, JPMorganChase, New York, NY, 10017, USA
| | - Marco Pistoia
- Global Technology Applied Research, JPMorganChase, New York, NY, 10017, USA
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2
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Smaldone AM, Batista VS. Quantum-to-Classical Neural Network Transfer Learning Applied to Drug Toxicity Prediction. J Chem Theory Comput 2024; 20:4901-4908. [PMID: 38795030 DOI: 10.1021/acs.jctc.4c00432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/27/2024]
Abstract
Toxicity is a roadblock that prevents an inordinate number of drugs from being used in potentially life-saving applications. Deep learning provides a promising solution to finding ideal drug candidates; however, the vastness of chemical space coupled with the underlying O ( n 3 ) matrix multiplication means these efforts quickly become computationally demanding. To remedy this, we present a hybrid quantum-classical neural network for predicting drug toxicity utilizing a quantum circuit design that mimics classical neural behavior by explicitly calculating matrix products with complexity O ( n 2 ) . Leveraging the Hadamard test for efficient inner product estimation rather than the conventionally used swap test, we reduce the number of qubits by half and remove the need for quantum phase estimation. Directly computing matrix products quantum mechanically allows for learnable weights to be transferred from a quantum to a classical device for further training. We apply our framework to the Tox21 data set and show that it achieves commensurate predictive accuracy to the model's fully classical O ( n 3 ) analogue. Additionally, we demonstrate that the model continues to learn, without disruption, once transferred to a fully classical architecture. We believe that combining the quantum advantage of reduced complexity and the classical advantage of noise-free calculation will pave the way for more scalable machine learning models.
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Affiliation(s)
- Anthony M Smaldone
- Department of Chemistry, Yale University, New Haven 06511, Connecticut, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven 06511, Connecticut, United States
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3
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Olarte Hernandez R, Champagne B, Soldera A. Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator. J Phys Chem A 2024; 128:4369-4377. [PMID: 38751235 DOI: 10.1021/acs.jpca.4c01234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/31/2024]
Abstract
In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H2O, SO2, ClO2, HS2, and ZnOH. The method solves the classically hard problem of estimating the Franck-Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
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Affiliation(s)
- Renato Olarte Hernandez
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
| | - Benoît Champagne
- Theoretical Chemistry Lab, Unit of Theoretical and Structural Physical Chemistry, Namur Institute of Structured Matter, University of Namur, rue de Bruxelles 61, B-5000 Namur, Belgium
| | - Armand Soldera
- Laboratory of Physical Chemistry of Matter, Department of Chemistry, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada
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4
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Qin H, Che L, Wei C, Xu F, Huang Y, Xin T. Experimental Direct Quantum Fidelity Learning via a Data-Driven Approach. PHYSICAL REVIEW LETTERS 2024; 132:190801. [PMID: 38804925 DOI: 10.1103/physrevlett.132.190801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 03/11/2024] [Indexed: 05/29/2024]
Abstract
Fidelity estimation is an important technique for evaluating prepared quantum states in noisy quantum devices. A recent theoretical work proposed a frugal approach called neural quantum fidelity estimation (NQFE) [X. Zhang et al., Phys. Rev. Lett. 127, 130503 (2021).PRLTAO0031-900710.1103/PhysRevLett.127.130503]. While this requires a much smaller number of measurement operators than full quantum state tomography, it uses a weight-based floating measurement strategy that predetermines the top global Pauli operators that contribute the most to the fidelity and uses discrete fidelity intervals as predictions. In this Letter, we develop a measurement-fixed NQFE based on a transformer model which requires less measurement cost and can output continuous estimates of fidelity. Here we further experimentally apply the NQFE in a realistic situation using a nuclear spin quantum processor. We prepare the ground states of local Hamiltonians and arbitrary states and investigate how to estimate their fidelity with reference states, and we compare the fidelity estimation strategy with our and the original NQFE to conventional tomography. It is shown that NQFE can estimate the fidelity with comparable accuracy to the tomography approach. In the future, NQFE will become an important tool for benchmarking quantum states ahead of the advent of well-trusted fault-tolerant quantum computers.
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Affiliation(s)
- Haiyang Qin
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Liangyu Che
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Chao Wei
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Feng Xu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yulei Huang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Tao Xin
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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5
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Litwin P, Wroński J, Markowski K, Lopez-Mago D, Masajada J, Szatkowski M. Ternary logic in the optical controlled-SWAP gate based on Laguerre-Gaussian modes of light. OPTICS EXPRESS 2024; 32:15258-15268. [PMID: 38859181 DOI: 10.1364/oe.520438] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/20/2024] [Indexed: 06/12/2024]
Abstract
The need set by a computational industry to increase processing power, while simultaneously reducing the energy consumption of data centers, became a challenge for modern computational systems. In this work, we propose an optical communication solution, that could serve as a building block for future computing systems, due to its versatility. The solution arises from Landauer's principle and utilizes reversible logic, manifested as an optical logical gate with structured light, here represented as Laguerre-Gaussian modes. We introduced a phase-shift-based encoding technique and incorporated multi-valued logic in the form of a ternary numeral system to determine the similarity between two images through the free space communication protocol.
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6
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Liu YK, Moody D. Post-quantum cryptography and the quantum future of cybersecurity. PHYSICAL REVIEW APPLIED 2024; 21:10.1103/physrevapplied.21.040501. [PMID: 38846721 PMCID: PMC11155471 DOI: 10.1103/physrevapplied.21.040501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2024]
Abstract
We review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum technologies might be used to enhance cybersecurity in the near future and beyond. We focus on two goals: protecting the secret keys that are used in classical cryptography, and ensuring the trustworthiness of quantum computations. These goals may soon be within reach, thanks to recent progress in both theory and experiment. This progress includes interactive protocols for testing quantumness as well as for performing uncloneable cryptographic computations; and experimental demonstrations of device-independent random number generators, device-independent quantum key distribution, quantum memories, and analog quantum simulators.
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Affiliation(s)
- Yi-Kai Liu
- National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
- Joint Center for Quantum Information and Computer Science (QuICS), NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Dustin Moody
- National Institute of Standards and Technology (NIST), Gaithersburg, Maryland 20899, USA
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7
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Henderson JM, Kath J, Golden JK, Percus AG, O'Malley D. Addressing quantum's "fine print" with efficient state preparation and information extraction for quantum algorithms and geologic fracture networks. Sci Rep 2024; 14:3592. [PMID: 38351145 PMCID: PMC10864371 DOI: 10.1038/s41598-024-52759-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 01/23/2024] [Indexed: 02/16/2024] Open
Abstract
Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum algorithms require that problems satisfy not only algorithm-specific constraints, but also application-specific ones. Otherwise, the quantum advantage carefully attained through algorithmic ingenuity can be entirely negated. Previous work addressing quantum algorithms for geologic fracture flow has illustrated core algorithmic approaches while incrementally removing assumptions. This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction. Our approach to addressing each is consistent with an overall exponential speed-up.
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Affiliation(s)
| | - John Kath
- Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, 91711, USA
| | - John K Golden
- Los Alamos National Laboratory, CCS-3, Los Alamos, NM, 87545, USA
| | - Allon G Percus
- Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, 91711, USA
| | - Daniel O'Malley
- Los Alamos National Laboratory, EES-16, Los Alamos, NM, 87545, USA
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8
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Volkmann H, Sathyanarayanan R, Saenz A, Jansen K, Kühn S. Chemically Accurate Potential Curves for H 2 Molecules Using Explicitly Correlated Qubit-ADAPT. J Chem Theory Comput 2024. [PMID: 38215397 DOI: 10.1021/acs.jctc.3c01281] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2024]
Abstract
With the recent advances in the development of devices capable of performing quantum computations, a growing interest in finding near-term applications has emerged in many areas of science. In the era of nonfault tolerant quantum devices, algorithms that only require comparably short circuits accompanied by high repetition rates are considered to be a promising approach for assisting classical machines with finding a solution on computationally hard problems. The ADAPT approach previously introduced in Nat. Commun. 10, 3007 (2019) extends the class of variational quantum eigensolver algorithms with dynamically growing ansätze in order to find approximations to the ground and excited state energies of molecules. In this work, the ADAPT algorithm has been combined with a first-quantized formulation for the hydrogen molecule in the Born-Oppenheimer approximation, employing the explicitly correlated basis functions introduced in J. Chem. Phys. 43, 2429 (1965). By the virtue of their explicit electronic correlation properties, it is shown in classically performed simulations that chemical accuracy (<1.6 mHa) can be reached for ground and excited state potential curves using reasonably short circuits.
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Affiliation(s)
- Hakon Volkmann
- AG Moderne Optik, Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Raamamurthy Sathyanarayanan
- AG Moderne Optik, Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Alejandro Saenz
- AG Moderne Optik, Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Karl Jansen
- CQTA, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
- Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus
| | - Stefan Kühn
- CQTA, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
- Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121 Nicosia, Cyprus
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9
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Zardini E, Blanzieri E, Pastorello D. Implementation and empirical evaluation of a quantum machine learning pipeline for local classification. PLoS One 2023; 18:e0287869. [PMID: 37956147 PMCID: PMC10642797 DOI: 10.1371/journal.pone.0287869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 06/14/2023] [Indexed: 11/15/2023] Open
Abstract
In the current era, quantum resources are extremely limited, and this makes difficult the usage of quantum machine learning (QML) models. Concerning the supervised tasks, a viable approach is the introduction of a quantum locality technique, which allows the models to focus only on the neighborhood of the considered element. A well-known locality technique is the k-nearest neighbors (k-NN) algorithm, of which several quantum variants have been proposed; nevertheless, they have not been employed yet as a preliminary step of other QML models. Instead, for the classical counterpart, a performance enhancement with respect to the base models has already been proven. In this paper, we propose and evaluate the idea of exploiting a quantum locality technique to reduce the size and improve the performance of QML models. In detail, we provide (i) an implementation in Python of a QML pipeline for local classification and (ii) its extensive empirical evaluation. Regarding the quantum pipeline, it has been developed using Qiskit, and it consists of a quantum k-NN and a quantum binary classifier, both already available in the literature. The results have shown the quantum pipeline's equivalence (in terms of accuracy) to its classical counterpart in the ideal case, the validity of locality's application to the QML realm, but also the strong sensitivity of the chosen quantum k-NN to probability fluctuations and the better performance of classical baseline methods like the random forest.
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Affiliation(s)
- Enrico Zardini
- Department of Information Engineering and Computer Science, University of Trento, Trento, Italy
| | - Enrico Blanzieri
- Department of Information Engineering and Computer Science, University of Trento, Trento, Italy
- Trento Institute for Fundamental Physics and Applications, Trento, Italy
| | - Davide Pastorello
- Department of Information Engineering and Computer Science, University of Trento, Trento, Italy
- Trento Institute for Fundamental Physics and Applications, Trento, Italy
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10
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Viladomat Jasso A, Modi A, Ferrara R, Deppe C, Nötzel J, Fung F, Schädler M. Quantum and Quantum-Inspired Stereographic K Nearest-Neighbour Clustering. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1361. [PMID: 37761660 PMCID: PMC10527652 DOI: 10.3390/e25091361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2023] [Revised: 09/12/2023] [Accepted: 09/13/2023] [Indexed: 09/29/2023]
Abstract
Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed 'quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.
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Affiliation(s)
- Alonso Viladomat Jasso
- Theoretical Quantum System Design Group, Chair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, Germany;
| | - Ark Modi
- Institute for Communications Engineering, TUM School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany; (R.F.); (C.D.)
| | - Roberto Ferrara
- Institute for Communications Engineering, TUM School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany; (R.F.); (C.D.)
| | - Christian Deppe
- Institute for Communications Engineering, TUM School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany; (R.F.); (C.D.)
| | - Janis Nötzel
- Theoretical Quantum System Design Group, Chair of Theoretical Information Technology, Technical University of Munich, 80333 Munich, Germany;
| | - Fred Fung
- Optical and Quantum Laboratory, Munich Research Center, Huawei Technologies Düsseldorf GmbH, Riesstr. 25-C3, 80992 Munich, Germany; (F.F.); (M.S.)
| | - Maximilian Schädler
- Optical and Quantum Laboratory, Munich Research Center, Huawei Technologies Düsseldorf GmbH, Riesstr. 25-C3, 80992 Munich, Germany; (F.F.); (M.S.)
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11
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Kim Y, Krylov AI. Two Algorithms for Excited-State Quantum Solvers: Theory and Application to EOM-UCCSD. J Phys Chem A 2023; 127:6552-6566. [PMID: 37505075 DOI: 10.1021/acs.jpca.3c02480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Near-term quantum devices promise to revolutionize quantum chemistry, but simulations using the current noisy intermediate-scale quantum (NISQ) devices are not practical due to their high susceptibility to errors. This motivated the design of NISQ algorithms leveraging classical and quantum resources. While several developments have shown promising results for ground-state simulations, extending the algorithms to excited states remains challenging. This paper presents two cost-efficient excited-state algorithms inspired by the classical Davidson algorithm. We implemented the Davidson method into the quantum self-consistent equation-of-motion unitary coupled-cluster (q-sc-EOM-UCC) excited-state method adapted for quantum hardware. The circuit strategies for generating desired excited states are discussed, implemented, and tested. We demonstrate the performance and accuracy of the proposed algorithms (q-sc-EOM-UCC/Davidson and its variational variant) by simulations of H2, H4, LiH, and H2O molecules. Similar to the classical Davidson scheme, q-sc-EOM-UCC/Davidson algorithms are capable of targeting a small number of excited states of the desired character.
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Affiliation(s)
- Yongbin Kim
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, United States
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12
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Caro MC, Huang HY, Ezzell N, Gibbs J, Sornborger AT, Cincio L, Coles PJ, Holmes Z. Out-of-distribution generalization for learning quantum dynamics. Nat Commun 2023; 14:3751. [PMID: 37407571 DOI: 10.1038/s41467-023-39381-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2022] [Accepted: 06/09/2023] [Indexed: 07/07/2023] Open
Abstract
Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.
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Affiliation(s)
- Matthias C Caro
- Department of Mathematics, Technical University of Munich, Garching, Germany.
- Munich Center for Quantum Science and Technology (MCQST), Munich, Germany.
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany.
- Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA.
| | - Hsin-Yuan Huang
- Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA
- Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA
| | - Nicholas Ezzell
- Information Sciences, Los Alamos National Laboratory, Los Alamos, NM, USA
- Department of Physics & Astronomy, University of Southern California, Los Angeles, CA, USA
| | - Joe Gibbs
- Department of Physics, University of Surrey, Guildford, GU2 7XH, UK
- AWE, Aldermaston, Reading, RG7 4PR, UK
| | | | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Patrick J Coles
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
- Normal Computing Corporation, New York, NY, USA
| | - Zoë Holmes
- Information Sciences, Los Alamos National Laboratory, Los Alamos, NM, USA
- Institute of Physics, Ecole Polytechnique Fédéderale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland
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13
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Illa M, Savage MJ. Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems. PHYSICAL REVIEW LETTERS 2023; 130:221003. [PMID: 37327435 DOI: 10.1103/physrevlett.130.221003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 04/27/2023] [Accepted: 04/28/2023] [Indexed: 06/18/2023]
Abstract
The time evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle rescalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.
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Affiliation(s)
- Marc Illa
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - Martin J Savage
- InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA
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14
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Wu YD, Zhu Y, Bai G, Wang Y, Chiribella G. Quantum Similarity Testing with Convolutional Neural Networks. PHYSICAL REVIEW LETTERS 2023; 130:210601. [PMID: 37295121 DOI: 10.1103/physrevlett.130.210601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/08/2023] [Accepted: 04/25/2023] [Indexed: 06/12/2023]
Abstract
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous variable quantum systems. In this Letter, we develop a machine learning algorithm for comparing unknown continuous variable states using limited and noisy data. The algorithm works on non-Gaussian quantum states for which similarity testing could not be achieved with previous techniques. Our approach is based on a convolutional neural network that assesses the similarity of quantum states based on a lower-dimensional state representation built from measurement data. The network can be trained off-line with classically simulated data from a fiducial set of states sharing structural similarities with the states to be tested, with experimental data generated by measurements on the fiducial states, or with a combination of simulated and experimental data. We test the performance of the model on noisy cat states and states generated by arbitrary selective number-dependent phase gates. Our network can also be applied to the problem of comparing continuous variable states across different experimental platforms, with different sets of achievable measurements, and to the problem of experimentally testing whether two states are equivalent up to Gaussian unitary transformations.
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Affiliation(s)
- Ya-Dong Wu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Yan Zhu
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
| | - Ge Bai
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
| | - Yuexuan Wang
- Department of Computer Science, AI Technology Laboratory, The University of Hong Kong, Pokfulam Road, Hong Kong
- College of Computer Science and Technology, Zhejiang University, Zhejiang Province 310058, China
| | - Giulio Chiribella
- Department of Computer Science, QICI Quantum Information and Computation Initiative, The University of Hong Kong, Pokfulam Road, Hong Kong
- Department of Computer Science, Parks Road, Oxford OX1 3QD, United Kingdom
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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15
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Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
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Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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16
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Engelsberger A, Villmann T. Quantum Computing Approaches for Vector Quantization-Current Perspectives and Developments. ENTROPY (BASEL, SWITZERLAND) 2023; 25:540. [PMID: 36981428 PMCID: PMC10048050 DOI: 10.3390/e25030540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Revised: 03/15/2023] [Accepted: 03/20/2023] [Indexed: 06/18/2023]
Abstract
In the field of machine learning, vector quantization is a category of low-complexity approaches that are nonetheless powerful for data representation and clustering or classification tasks. Vector quantization is based on the idea of representing a data or a class distribution using a small set of prototypes, and hence, it belongs to interpretable models in machine learning. Further, the low complexity of vector quantizers makes them interesting for the application of quantum concepts for their implementation. This is especially true for current and upcoming generations of quantum devices, which only allow the execution of simple and restricted algorithms. Motivated by different adaptation and optimization paradigms for vector quantizers, we provide an overview of respective existing quantum algorithms and routines to realize vector quantization concepts, maybe only partially, on quantum devices. Thus, the reader can infer the current state-of-the-art when considering quantum computing approaches for vector quantization.
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17
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Chan HHS, Meister R, Jones T, Tew DP, Benjamin SC. Grid-based methods for chemistry simulations on a quantum computer. SCIENCE ADVANCES 2023; 9:eabo7484. [PMID: 36857445 PMCID: PMC9977186 DOI: 10.1126/sciadv.abo7484] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.
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Affiliation(s)
| | - Richard Meister
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - Tyson Jones
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
| | - David P. Tew
- Department of Chemistry, University of Oxford, Oxford OX1 3TA, UK
- Duality Quantum Photonics, 6 Lower Park Row, Bristol BS1 5BJ, UK
| | - Simon C. Benjamin
- Department of Materials, University of Oxford, Oxford OX1 3PH, UK
- Quantum Motion, 9 Sterling Way, London N7 9HJ, UK
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18
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Gupta S, Saha D, Xu ZP, Cabello A, Majumdar AS. Quantum Contextuality Provides Communication Complexity Advantage. PHYSICAL REVIEW LETTERS 2023; 130:080802. [PMID: 36898100 DOI: 10.1103/physrevlett.130.080802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 01/31/2023] [Indexed: 06/18/2023]
Abstract
Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimensions producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device-independent protocol for quantum key distribution.
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Affiliation(s)
- Shashank Gupta
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Debashis Saha
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, 230601 Hefei, People's Republic of China
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - A S Majumdar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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19
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Wang XW, Zhou WH, Fu YX, Gao J, Lu YH, Chang YJ, Qiao LF, Ren RJ, Jiang ZK, Jiao ZQ, Nikolopoulos GM, Jin XM. Experimental Boson Sampling Enabling Cryptographic One-Way Function. PHYSICAL REVIEW LETTERS 2023; 130:060802. [PMID: 36827576 DOI: 10.1103/physrevlett.130.060802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Boson sampling is a computational problem, which is commonly believed to be a representative paradigm for attaining the milestone of quantum advantage. So far, massive efforts have been made to the experimental large-scale boson sampling for demonstrating this milestone, while further applications of the machines remain a largely unexplored area. Here, we investigate experimentally the efficiency and security of a cryptographic one-way function that relies on coarse-grained boson sampling, in the framework of a photonic boson-sampling machine fabricated by a femtosecond laser direct writing technique. Our findings demonstrate that the implementation of the function requires moderate sample sizes, which can be over 4 orders of magnitude smaller than the ones predicted by the Chernoff bound; whereas for numbers of photons n≥3 and bins d∼poly(m,n), the same output of the function cannot be generated by nonboson samplers. Our Letter is the first experimental study that deals with the potential applications of boson sampling in the field of cryptography and paves the way toward additional studies in this direction.
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Affiliation(s)
- Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Yu-Xuan Fu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Jun Gao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Yong-Heng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Yi-Jun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Lu-Feng Qiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Ruo-Jing Ren
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Ze-Kun Jiang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | - Zhi-Qiang Jiao
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
| | | | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
- Hefei National Laboratory, Hefei 230088, China
- TuringQ Company, Ltd., Shanghai 200240, China
- Chip Hub for Integrated Photonics Xplore (CHIPX), Shanghai Jiao Tong University, Wuxi 214000, China
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20
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Zhang X, Kim E, Mark DK, Choi S, Painter O. A superconducting quantum simulator based on a photonic-bandgap metamaterial. Science 2023; 379:278-283. [PMID: 36656924 DOI: 10.1126/science.ade7651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Synthesizing many-body quantum systems with various ranges of interactions facilitates the study of quantum chaotic dynamics. Such extended interaction range can be enabled by using nonlocal degrees of freedom such as photonic modes in an otherwise locally connected structure. Here, we present a superconducting quantum simulator in which qubits are connected through an extensible photonic-bandgap metamaterial, thus realizing a one-dimensional Bose-Hubbard model with tunable hopping range and on-site interaction. Using individual site control and readout, we characterize the statistics of measurement outcomes from many-body quench dynamics, which enables in situ Hamiltonian learning. Further, the outcome statistics reveal the effect of increased hopping range, showing the predicted crossover from integrability to ergodicity. Our work enables the study of emergent randomness from chaotic many-body evolution and, more broadly, expands the accessible Hamiltonians for quantum simulation using superconducting circuits.
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Affiliation(s)
- Xueyue Zhang
- Thomas J. Watson, Sr., Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA
| | - Eunjong Kim
- Thomas J. Watson, Sr., Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA
| | - Daniel K Mark
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Soonwon Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Oskar Painter
- Thomas J. Watson, Sr., Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125, USA.,Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125, USA.,AWS Center for Quantum Computing, Pasadena, CA 91125, USA
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21
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Feng C, Zhao B, Zhou X, Ding X, Shan Z. An Enhanced Quantum K-Nearest Neighbor Classification Algorithm Based on Polar Distance. ENTROPY (BASEL, SWITZERLAND) 2023; 25:127. [PMID: 36673268 PMCID: PMC9857881 DOI: 10.3390/e25010127] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Revised: 01/04/2023] [Accepted: 01/04/2023] [Indexed: 06/17/2023]
Abstract
The K-nearest neighbor (KNN) algorithm is one of the most extensively used classification algorithms, while its high time complexity limits its performance in the era of big data. The quantum K-nearest neighbor (QKNN) algorithm can handle the above problem with satisfactory efficiency; however, its accuracy is sacrificed when directly applying the traditional similarity measure based on Euclidean distance. Inspired by the Polar coordinate system and the quantum property, this work proposes a new similarity measure to replace the Euclidean distance, which is defined as Polar distance. Polar distance considers both angular and module length information, introducing a weight parameter adjusted to the specific application data. To validate the efficiency of Polar distance, we conducted various experiments using several typical datasets. For the conventional KNN algorithm, the accuracy performance is comparable when using Polar distance for similarity measurement, while for the QKNN algorithm, it significantly outperforms the Euclidean distance in terms of classification accuracy. Furthermore, the Polar distance shows scalability and robustness superior to the Euclidean distance, providing an opportunity for the large-scale application of QKNN in practice.
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Affiliation(s)
- Congcong Feng
- School of Cyber Science and Engineering, Zhengzhou University, Zhengzhou 450002, China
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
| | - Bo Zhao
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Songshan Laboratory, Zhengzhou 450001, China
| | - Xin Zhou
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
| | - Xiaodong Ding
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
| | - Zheng Shan
- State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
- Songshan Laboratory, Zhengzhou 450001, China
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22
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Xue S, Wang Y, Liu Y, Shi W, Wu J. Variational Quantum Process Tomography of Non-Unitaries. ENTROPY (BASEL, SWITZERLAND) 2023; 25:90. [PMID: 36673231 PMCID: PMC9858050 DOI: 10.3390/e25010090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Revised: 12/26/2022] [Accepted: 12/27/2022] [Indexed: 06/17/2023]
Abstract
Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (d≤8), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators.
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Affiliation(s)
| | | | | | | | - Junjie Wu
- Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
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23
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Anschuetz ER, Kiani BT. Quantum variational algorithms are swamped with traps. Nat Commun 2022; 13:7760. [PMID: 36522354 PMCID: PMC9755303 DOI: 10.1038/s41467-022-35364-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 11/30/2022] [Indexed: 12/23/2022] Open
Abstract
One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that unlike the case in classical neural networks, variational quantum models are often not trainable. The most studied phenomenon is the onset of barren plateaus in the training landscape of these quantum models, typically when the models are very deep. This focus on barren plateaus has made the phenomenon almost synonymous with the trainability of quantum models. Here, we show that barren plateaus are only a part of the story. We prove that a wide class of variational quantum models-which are shallow, and exhibit no barren plateaus-have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known. We also study the trainability of variational quantum algorithms from a statistical query framework, and show that noisy optimization of a wide variety of quantum models is impossible with a sub-exponential number of queries. Finally, we numerically confirm our results on a variety of problem instances. Though we exclude a wide variety of quantum algorithms here, we give reason for optimism for certain classes of variational algorithms and discuss potential ways forward in showing the practical utility of such algorithms.
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Affiliation(s)
- Eric R Anschuetz
- MIT Center for Theoretical Physics, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA.
| | - Bobak T Kiani
- MIT Department of Electrical Engineering and Computer Science, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA.
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24
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Tello Castillo A, Donaldson R. Time-division technique for quantum optical receivers utilizing single-photon detector array technology and spatial-multiplexing. OPTICS EXPRESS 2022; 30:44365-44374. [PMID: 36522862 DOI: 10.1364/oe.470364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Free-space quantum key distribution (QKD) has been gaining popularity in recent years due to its advantages in creating networking options for the quantum internet. One of the main challenges to be addressed in QKD is the achievable secret key rate, which must meet current and future demand. Some of the existing solutions include the use of higher bandwidth electronics, untrusted relay architectures such as Twin-Field QKD, or high dimensional QKD. In this work, we proposed the use of a combination of spatial-multiplexing and time-division techniques, together with the use of 2D single-photon avalanche diode arrays to increase the final throughput. The main challenge in a free-space scenario is the effects introduced by turbulence. This paper demonstrates how appropriate time-division of the spatial-modes can reduce the quantum bit error rate due to optical crosstalk from 36% to 0%. With this technique, we believe the future need for superconducting nanowires single photon detectors, in some free-space QKD applications, can be relaxed, obtaining more cost-effective receiver systems.
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25
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Ding Y, Ban Y, Chen X. Towards Quantum Control with Advanced Quantum Computing: A Perspective. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1743. [PMID: 36554148 PMCID: PMC9777876 DOI: 10.3390/e24121743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 11/24/2022] [Accepted: 11/25/2022] [Indexed: 06/17/2023]
Abstract
We propose the combination of digital quantum simulation and variational quantum algorithms as an alternative approach to numerical methods for solving quantum control problems. As a hybrid quantum-classical framework, it provides an efficient simulation of quantum dynamics compared to classical algorithms, exploiting the previous achievements in digital quantum simulation. We analyze the trainability and the performance of such algorithms based on our preliminary works. We show that specific quantum control problems, e.g., finding the switching time for bang-bang control or the digital quantum annealing schedule, can already be studied in the noisy intermediate-scale quantum era. We foresee that these algorithms will contribute even more to quantum control of high precision if the hardware for experimental implementation is developed to the next level.
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Affiliation(s)
- Yongcheng Ding
- International Center of Quantum Artificial Intelligence for Science and Technology (QuArtist) and Department of Physics, Shanghai University, Shanghai 200444, China
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - Yue Ban
- TECNALIA, Basque Research and Technology Alliance (BRTA), 48160 Derio, Spain
| | - Xi Chen
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- EHU Quantum Center, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
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26
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Zhu D, Cian ZP, Noel C, Risinger A, Biswas D, Egan L, Zhu Y, Green AM, Alderete CH, Nguyen NH, Wang Q, Maksymov A, Nam Y, Cetina M, Linke NM, Hafezi M, Monroe C. Cross-platform comparison of arbitrary quantum states. Nat Commun 2022; 13:6620. [PMID: 36333309 PMCID: PMC9636372 DOI: 10.1038/s41467-022-34279-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 10/18/2022] [Indexed: 11/06/2022] Open
Abstract
As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information of executing specific tasks for a single QC. On the other hand, a comparison between different QCs preparing nominally the same arbitrary circuit provides an insight for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform state fidelities.
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Affiliation(s)
- D Zhu
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA
- IonQ, College Park, MD, 20740, USA
| | - Z P Cian
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA.
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA.
- Department of Physics, University of Maryland, College Park, MD, 20742, USA.
| | - C Noel
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
- Duke Quantum Center and Department of Physics, Duke University, Durham, NC, 27708, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA
| | - A Risinger
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA
| | - D Biswas
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - L Egan
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - Y Zhu
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - A M Green
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - C Huerta Alderete
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - N H Nguyen
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - Q Wang
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Chemical Physics Program and Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA
| | | | - Y Nam
- IonQ, College Park, MD, 20740, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - M Cetina
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
- Duke Quantum Center and Department of Physics, Duke University, Durham, NC, 27708, USA
| | - N M Linke
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - M Hafezi
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
| | - C Monroe
- Joint Quantum Institute, University of Maryland, College Park, MD, 20742, USA
- Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA
- IonQ, College Park, MD, 20740, USA
- Department of Physics, University of Maryland, College Park, MD, 20742, USA
- Duke Quantum Center and Department of Physics, Duke University, Durham, NC, 27708, USA
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA
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27
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Salehi T, Zomorodi M, Plawiak P, Abbaszade M, Salari V. An optimizing method for performance and resource utilization in quantum machine learning circuits. Sci Rep 2022; 12:16949. [PMID: 36216853 PMCID: PMC9551098 DOI: 10.1038/s41598-022-20375-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Accepted: 09/13/2022] [Indexed: 11/16/2022] Open
Abstract
Quantum computing is a new and advanced topic that refers to calculations based on the principles of quantum mechanics. It makes certain kinds of problems be solved easier compared to classical computers. This advantage of quantum computing can be used to implement many existing problems in different fields incredibly effectively. One important field that quantum computing has shown great results in machine learning. Until now, many different quantum algorithms have been presented to perform different machine learning approaches. In some special cases, the execution time of these quantum algorithms will be reduced exponentially compared to the classical ones. But at the same time, with increasing data volume and computation time, taking care of systems to prevent unwanted interactions with the environment can be a daunting task and since these algorithms work on machine learning problems, which usually includes big data, their implementation is very costly in terms of quantum resources. Here, in this paper, we have proposed an approach to reduce the cost of quantum circuits and to optimize quantum machine learning circuits in particular. To reduce the number of resources used, in this paper an approach including different optimization algorithms is considered. Our approach is used to optimize quantum machine learning algorithms for big data. In this case, the optimized circuits run quantum machine learning algorithms in less time than the original ones and by preserving the original functionality. Our approach improves the number of quantum gates by 10.7% and 14.9% in different circuits respectively. This is the amount of reduction for one iteration of a given sub-circuit U in the main circuit. For cases where this sub-circuit is repeated more times in the main circuit, the optimization rate is increased. Therefore, by applying the proposed method to circuits with big data, both cost and performance are improved.
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Affiliation(s)
- Tahereh Salehi
- Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
| | - Mariam Zomorodi
- Department of Computer Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.
- Department of Computer Science, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Krakow, Poland.
| | - Pawel Plawiak
- Department of Computer Science, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Krakow, Poland
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Gliwice, Poland
| | - Mina Abbaszade
- Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111, Iran
| | - Vahid Salari
- Institute for Quantum Science and Technology, and Department of Physics and Astronomy, University of Calgary, Calgary, T2N 1N4, Alberta, Canada
- Basque Center for Applied Mathematics (BCAM), Bilbao, Spain
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28
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Sajjan M, Li J, Selvarajan R, Sureshbabu SH, Kale SS, Gupta R, Singh V, Kais S. Quantum machine learning for chemistry and physics. Chem Soc Rev 2022; 51:6475-6573. [PMID: 35849066 DOI: 10.1039/d2cs00203e] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Machine learning (ML) has emerged as a formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In recent years, it is safe to conclude that ML and its close cousin, deep learning (DL), have ushered in unprecedented developments in all areas of physical sciences, especially chemistry. Not only classical variants of ML, even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionized materials design and performance of photovoltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is not only to foster exposition of the aforesaid techniques but also to empower and promote cross-pollination among future research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Junxu Li
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Raja Selvarajan
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA
| | - Shree Hari Sureshbabu
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
| | - Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Vinit Singh
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, IN-47907, USA. .,Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA.,Department of Physics and Astronomy, Purdue University, West Lafayette, IN-47907, USA.,Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN-47907, USA
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29
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Accelerating spiking neural networks using quantum algorithm with high success probability and high calculation accuracy. Neurocomputing 2022. [DOI: 10.1016/j.neucom.2022.02.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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30
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Quantum Linear System Algorithm for General Matrices in System Identification. ENTROPY 2022; 24:e24070893. [PMID: 35885115 PMCID: PMC9323527 DOI: 10.3390/e24070893] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 06/24/2022] [Accepted: 06/25/2022] [Indexed: 01/27/2023]
Abstract
Solving linear systems of equations is one of the most common and basic problems in classical identification systems. Given a coefficient matrix A and a vector b, the ultimate task is to find the solution x such that Ax=b. Based on the technique of the singular value estimation, the paper proposes a modified quantum scheme to obtain the quantum state |x〉 corresponding to the solution of the linear system of equations in O(κ2rpolylog(mn)/ϵ) time for a general m×n dimensional A, which is superior to existing quantum algorithms, where κ is the condition number, r is the rank of matrix A and ϵ is the precision parameter. Meanwhile, we also design a quantum circuit for the homogeneous linear equations and achieve an exponential improvement. The coefficient matrix A in our scheme is a sparsity-independent and non-square matrix, which can be applied in more general situations. Our research provides a universal quantum linear system solver and can enrich the research scope of quantum computation.
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31
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Abstract
This paper presents a theoretical study into the use of optical systems for quantum computation. The study results pertain to quantum sampling and quantum communication and provide a basis for further research and the development of a physical implementation. We propose an optical superstructure that can implement specific computation processes and algorithms. The superstructure is composed of nonlinear optical units, such as beta barium borate crystals. The units are positioned in series, powered by a pulse laser pump, and culminate in a beam splitter that generates the output state of a number of entangled photon pairs. Computation is achieved by entanglement propagation via beam splitters and adjustable phase shifters, which set related parameters. Demonstrating a two-component case, we show how a series of cosine-based components can be implemented. The obtained results open a broad front for future research. Future work should investigate the construction of a quantum optimizer using quantum sampling methods and also investigate high-precision temporal voltage measurement, which is a key procedure for the construction of high-fidelity devices.
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32
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Faster quantum ridge regression algorithm for prediction. INT J MACH LEARN CYB 2022. [DOI: 10.1007/s13042-022-01526-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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Wu Z, Song T, Zhang Y. Quantum Density Peak Clustering Algorithm. ENTROPY 2022; 24:e24020237. [PMID: 35205530 PMCID: PMC8870877 DOI: 10.3390/e24020237] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Revised: 01/28/2022] [Accepted: 02/01/2022] [Indexed: 12/04/2022]
Abstract
A widely used clustering algorithm, density peak clustering (DPC), assigns different attribute values to data points through the distance between data points, and then determines the number and range of clustering by attribute values. However, DPC is inefficient when dealing with scenes with a large amount of data, and the range of parameters is not easy to determine. To fix these problems, we propose a quantum DPC (QDPC) algorithm based on a quantum DistCalc circuit and a Grover circuit. The time complexity is reduced to O(log(N2)+6N+N), whereas that of the traditional algorithm is O(N2). The space complexity is also decreased from O(N·⌈logN⌉) to O(⌈logN⌉).
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Affiliation(s)
- Zhihao Wu
- College of Cyber Security, Jinan University, Guangzhou 510632, China;
| | - Tingting Song
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China;
- Guangxi Key Laboratory of Cryptography and Information Security, Guilin 541004, China
- Correspondence:
| | - Yanbing Zhang
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China;
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34
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A Verifiable Arbitrated Quantum Signature Scheme Based on Controlled Quantum Teleportation. ENTROPY 2022; 24:e24010111. [PMID: 35052137 PMCID: PMC8774689 DOI: 10.3390/e24010111] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2021] [Revised: 01/08/2022] [Accepted: 01/09/2022] [Indexed: 12/04/2022]
Abstract
In this paper, we present a verifiable arbitrated quantum signature scheme based on controlled quantum teleportation. The five-qubit entangled state functions as a quantum channel. The proposed scheme uses mutually unbiased bases particles as decoy particles and performs unitary operations on these decoy particles, applying the functional values of symmetric bivariate polynomial. As such, eavesdropping detection and identity authentication can both be executed. The security analysis shows that our scheme can neither be disavowed by the signatory nor denied by the verifier, and it cannot be forged by any malicious attacker.
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35
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Policharla GV, Vinjanampathy S. Algorithmic Primitives for Quantum-Assisted Quantum Control. PHYSICAL REVIEW LETTERS 2021; 127:220504. [PMID: 34889622 DOI: 10.1103/physrevlett.127.220504] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Revised: 08/10/2021] [Accepted: 10/22/2021] [Indexed: 06/13/2023]
Abstract
We present two primitive algorithms to evaluate overlaps and transition matrix time series, which are then used to construct several quantum-assisted quantum control algorithms. Unlike previous approaches, our method bypasses tomographically complete measurements and instead relies solely on single qubit measurements. We analyze circuit complexity of composed algorithms and sources of noise arising from Trotterization and measurement errors.
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Affiliation(s)
- Guru-Vamsi Policharla
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
| | - Sai Vinjanampathy
- Department of Physics, Indian Institute of Technology-Bombay, Powai, Mumbai 400076, India
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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36
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Beckey JL, Gigena N, Coles PJ, Cerezo M. Computable and Operationally Meaningful Multipartite Entanglement Measures. PHYSICAL REVIEW LETTERS 2021; 127:140501. [PMID: 34652179 DOI: 10.1103/physrevlett.127.140501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 08/12/2021] [Indexed: 06/13/2023]
Abstract
Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state |ψ⟩ for these applications is often directly related to the degree or type of entanglement present in |ψ⟩. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.
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Affiliation(s)
- Jacob L Beckey
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- JILA, NIST and University of Colorado, Boulder, Colorado 80309, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Quantum Science Center, Oak Ridge, Tennessee 37931, USA
| | - N Gigena
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Patrick J Coles
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Quantum Science Center, Oak Ridge, Tennessee 37931, USA
| | - M Cerezo
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Quantum Science Center, Oak Ridge, Tennessee 37931, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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37
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Sugisaki K, Sakai C, Toyota K, Sato K, Shiomi D, Takui T. Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps. Phys Chem Chem Phys 2021; 23:20152-20162. [PMID: 34551045 DOI: 10.1039/d1cp03156b] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems. In the race of finding efficient quantum algorithms to solve quantum chemistry problems, we test a Bayesian phase difference estimation (BPDE) algorithm, which is a general algorithm to calculate the difference of two eigenphases of unitary operators in the several cases of the direct calculations of energy gaps between two electronic states on quantum computers, including vertical ionisation energies, singlet-triplet energy gaps, and vertical excitation energies. In the BPDE algorithm, state preparation is carried out conditionally on the ancillary qubit, and the time evolution of the wave functions in superposition of two electronic states are executed unconditionally. Based on our test, we conclude that BPDE is capable of computing the energy gap with an accuracy similar to BPE without controlled-time evolution simulations and with the smaller number of iterations in Bayesian optimisations.
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Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. .,JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan.,Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG CREST), 16th Floor, Omega, BIPL Building, Blocks EP & GP, Sector V, Salt Lake, Kolkata 700091, India
| | - Chikako Sakai
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Kazuo Toyota
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Kazunobu Sato
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Daisuke Shiomi
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
| | - Takeji Takui
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. .,Research Support Department/University Research Administrator Centre, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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38
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Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection. Nat Commun 2021; 12:4464. [PMID: 34294720 PMCID: PMC8298536 DOI: 10.1038/s41467-021-24745-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Accepted: 07/01/2021] [Indexed: 11/25/2022] Open
Abstract
Quantum communication complexity explores the minimum amount of communication required to achieve certain tasks using quantum states. One representative example is quantum fingerprinting, in which the minimum amount of communication could be exponentially smaller than the classical fingerprinting. Here, we propose a quantum fingerprinting protocol where coherent states and channel multiplexing are used, with simultaneous detection of signals carried by multiple channels. Compared with an existing coherent quantum fingerprinting protocol, our protocol could consistently reduce communication time and the amount of communication by orders of magnitude by increasing the number of channels. Our proposed protocol can even beat the classical limit without using superconducting-nanowire single photon detectors. We also report a proof-of-concept experimental demonstration with six wavelength channels to validate the advantage of our protocol in the amount of communication. The experimental results clearly prove that our protocol not only surpasses the best-known classical protocol, but also remarkably outperforms the existing coherent quantum fingerprinting protocol. Quantum fingerprinting could allow an exponential quantum advantage in a cryptographic protocol, but current schemes are still difficult to scale. Here, the authors exploit wavelength division multiplexing to increase the channel capacity and reduce the communication time without the need for demultiplexing.
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39
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Sugisaki K, Toyota K, Sato K, Shiomi D, Takui T. Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies. J Phys Chem Lett 2021; 12:2880-2885. [PMID: 33724039 DOI: 10.1021/acs.jpclett.1c00283] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies. Numerical quantum circuit simulations for the ionization of light atoms (He, Li, Be, B, C, and N) and small molecules (HF, BF, CF, CO, O2, NO, CN, F2, H2O, and NH3) revealed that the proposed quantum algorithm affords the vertical ionization energies within 0.1 eV of precision.
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Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- JST PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
- Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG CREST), 16th Floor, Omega, BIPL Building, Blocks EP & GP, Sector V, Salt Lake, Kolkata 700091, India
| | - Kazuo Toyota
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Kazunobu Sato
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Daisuke Shiomi
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
| | - Takeji Takui
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
- Research Support Department/University Research Administrator Center, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
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40
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Sugisaki K, Toyota K, Sato K, Shiomi D, Takui T. A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions. Chem Sci 2020; 12:2121-2132. [PMID: 34163976 PMCID: PMC8179312 DOI: 10.1039/d0sc04847j] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Accepted: 12/13/2020] [Indexed: 01/03/2023] Open
Abstract
The Heisenberg exchange coupling parameter J (H = -2J S i · S j ) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term j S 2, the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H2 under a covalent bond dissociation, C, O, Si, NH, OH+, CH2, NF, O2, and triple bond dissociated N2 molecule revealed that the BxB can compute the J value within 1 kcal mol-1 of errors with less computational costs than conventional quantum phase estimation-based approaches.
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Affiliation(s)
- Kenji Sugisaki
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
- JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan
| | - Kazuo Toyota
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
| | - Kazunobu Sato
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
| | - Daisuke Shiomi
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
| | - Takeji Takui
- Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
- Research Support Department, University Research Administrator Centre, University Administration Division, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan
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41
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Kathuria K, Ratan A, McConnell M, Bekiranov S. Implementation of a Hamming distance-like genomic quantum classifier using inner products on ibmqx2 and ibmq_16_melbourne. QUANTUM MACHINE INTELLIGENCE 2020; 2:1-26. [PMID: 32879908 PMCID: PMC7446251 DOI: 10.1007/s42484-020-00017-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Accepted: 05/01/2020] [Indexed: 06/11/2023]
Abstract
Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product-based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute's existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product-based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance-based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product-based classifier. The classifiers implement an inner product between N = 2 n dimension test and train vectors using n Fredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary number m of samples that can be classically summed into one input string to effectively execute all test-train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are O ( log N ) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.
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Affiliation(s)
- Kunal Kathuria
- Department of Biochemistry and Molecular Genetics, University of Virginia, Charlottesville, VA USA
| | - Aakrosh Ratan
- Center for Public Health Genomics, University of Virginia, Charlottesville, VA USA
| | - Michael McConnell
- Department of Biochemistry and Molecular Genetics, University of Virginia, Charlottesville, VA USA
| | - Stefan Bekiranov
- Department of Biochemistry and Molecular Genetics, University of Virginia, Charlottesville, VA USA
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42
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Li P, Wang B. Quantum neural networks model based on swap test and phase estimation. Neural Netw 2020; 130:152-164. [PMID: 32663639 DOI: 10.1016/j.neunet.2020.07.003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Revised: 05/11/2020] [Accepted: 07/03/2020] [Indexed: 11/17/2022]
Abstract
In this paper, a neural networks model for quantum computer is proposed. The core of this model is quantum neuron. Firstly, the inner product of the input qubits and the weight qubits is mapped to the phase of the control qubits in the neuron by the swap test technology, and then these phases are obtained by the phase estimation method, which are further used as the phase of the output qubit in the neuron. In this way, the mapping of input qubits to output qubit in quantum neuron is completed. The quantum neurons mentioned above can be used to construct quantum neural networks. In this paper, the quantum circuit for each operation step are given. The simulation results on the classic computer verify the effectiveness of the proposed model.
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Affiliation(s)
- Panchi Li
- School of Computer and Information Technology, Northeast Petroleum University, Daqing 163318, China.
| | - Bing Wang
- School of Computer and Information Technology, Northeast Petroleum University, Daqing 163318, China
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43
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Gan HCJ, Maslennikov G, Tseng KW, Nguyen C, Matsukevich D. Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System. PHYSICAL REVIEW LETTERS 2020; 124:170502. [PMID: 32412255 DOI: 10.1103/physrevlett.124.170502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.
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Affiliation(s)
- H C J Gan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Ko-Wei Tseng
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Chihuan Nguyen
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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44
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Urrego DF, Lopez-Mago D, Vicuña-Hernández V, Torres JP. Quantum-inspired Fredkin gate based on spatial modes of light. OPTICS EXPRESS 2020; 28:12661-12674. [PMID: 32403759 DOI: 10.1364/oe.384654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Accepted: 04/07/2020] [Indexed: 06/11/2023]
Abstract
Insights gained from quantum physics can inspire novel classical technologies. These quantum-inspired technologies are protocols that aim at mimicking particular features of quantum algorithms. They are generally easier to implement and make use of intense beams. Here we demonstrate in a proof-of-concept experiment a quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001).The carriers of information are optical beams with orbital angular momentum (OAM). These beams allow the implementation of a Fredkin gate or polarization-controlled SWAP operation that exchanges data encoded on beams with different OAM. We measure the degree of similarity between waveforms and strings of bits without unveiling the information content of the data.
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45
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Fanizza M, Rosati M, Skotiniotis M, Calsamiglia J, Giovannetti V. Beyond the Swap Test: Optimal Estimation of Quantum State Overlap. PHYSICAL REVIEW LETTERS 2020; 124:060503. [PMID: 32109123 DOI: 10.1103/physrevlett.124.060503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 12/11/2019] [Accepted: 12/12/2019] [Indexed: 06/10/2023]
Abstract
We study the estimation of the overlap between two unknown pure quantum states of a finite-dimensional system, given M and N copies of each type. This is a fundamental primitive in quantum information processing that is commonly accomplished from the outcomes of N swap tests, a joint measurement on one copy of each type whose outcome probability is a linear function of the squared overlap. We show that a more precise estimate can be obtained by allowing for general collective measurements on all copies. We derive the statistics of the optimal measurement and compute the optimal mean square error in the asymptotic pointwise and finite Bayesian estimation settings. Besides, we consider two strategies relying on the estimation of one or both states and show that, although they are suboptimal, they outperform the swap test. In particular, the swap test is extremely inefficient for small values of the overlap, which become exponentially more likely as the dimension increases. Finally, we show that the optimal measurement is less invasive than the swap test and study the robustness to depolarizing noise for qubit states.
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Affiliation(s)
- M Fanizza
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | - M Rosati
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - M Skotiniotis
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - J Calsamiglia
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - V Giovannetti
- NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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46
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Xin X, Wang Z, Yang Q. Quantum signature scheme based on Hadamard and H π/4 operators. APPLIED OPTICS 2019; 58:7346-7351. [PMID: 31674378 DOI: 10.1364/ao.58.007346] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 08/16/2019] [Indexed: 06/10/2023]
Abstract
Based on the Hadamard and Hπ/4 operators, a new quantum signature scheme is proposed. In our scheme, the signer's private key is generated by a trusted private key generator (PKG), while the identity information of the signer is used as the corresponding public key. Both of the private key and public key of the signer are classical bit strings, which can be easily stored and reused. Given a quantum signature, anyone can verify the validity of the quantum signature with the signer's identity. Therefore, our scheme is a public-key quantum signature without a digital certificate, which has the merits of an identity-based cryptosystem and can simplify the key management of the quantum signature system. On the other hand, our scheme need not use any quantum swap test during the signature verification phase. Furthermore, by the signature proof, our scheme can arbitrate the potential disputation of losing quantum signature, which cannot be arbitrated in most of the quantum signature schemes. So our scheme has the property of strong non-repudiation. It also has the security properties of information-theoretic security, unforgeability, etc. Our scheme can achieve a high efficiency of 70%. Therefore, our quantum signature scheme is more secure, practicable, and efficient than the similar schemes.
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47
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Kumar N, Kerenidis I, Diamanti E. Experimental demonstration of quantum advantage for one-way communication complexity surpassing best-known classical protocol. Nat Commun 2019; 10:4152. [PMID: 31515513 PMCID: PMC6742668 DOI: 10.1038/s41467-019-12139-z] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2018] [Accepted: 08/02/2019] [Indexed: 12/03/2022] Open
Abstract
Demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity offers the possibility to already explore and showcase this advantage for useful tasks. Here, we define such a task, the Sampling Matching problem, which is inspired by the Hidden Matching problem and features an exponential gap between quantum and classical protocols in the one-way communication model. Our problem allows by its conception a photonic implementation based on encoding in the phase of coherent states of light, the use of a fixed size linear optic circuit, and single-photon detection. This enables us to demonstrate in a proof-of-principle experiment an advantage in the transmitted information resource over the best known classical protocol, something impossible to reach for the original Hidden Matching problem. Our demonstration has implications in quantum verification and cryptographic settings. The hidden matching communication problem features an exponential classical-quantum gap, but a demonstration is extremely challenging. Here, the authors define a more feasible variant called sampling matching problem, and realise a proof-of-principle implementation beating the best known classical protocol.
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Affiliation(s)
- Niraj Kumar
- Sorbonne Université, CNRS, LIP6, F-75005, Paris, France. .,IRIF, CNRS, Université Paris Diderot, 75013, Paris, France.
| | | | - Eleni Diamanti
- Sorbonne Université, CNRS, LIP6, F-75005, Paris, France.
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48
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Li DX, Zheng TY, Shao XQ. Adiabatic preparation of Multipartite GHZ states via Rydberg ground-state blockade. OPTICS EXPRESS 2019; 27:20874-20885. [PMID: 31510175 DOI: 10.1364/oe.27.020874] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Accepted: 06/24/2019] [Indexed: 06/10/2023]
Abstract
The multipartite GHZ states are useful resources for quantum information processing. Here we put forward a scalable way to adiabatically prepare the multipartite GHZ states in a chain of Rydberg atoms. Building on the ground-state blockade effect of Rydberg atoms and the stimulated Raman adiabatic passage (STIRAP), we suppress the adverse effect of the atomic spontaneous emission, and obtain a high fidelity of the multipartite GHZ states without requirements on the operational time. After investigating the feasibility of the proposal, we show a 3-qubit GHZ state can be generated in a wide range of relevant parameters and a fidelity above $98\%$98% is achievable with the current experimental technologies.
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49
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Abstract
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
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Affiliation(s)
| | - Joonsuk Huh
- Department of Chemistry , Sungkyunkwan University , Suwon , Gyeonggi-do 16419 , Republic of Korea
- SKKU Advanced Institute of Nanotechnology (SAINT) , Sungkyunkwan University , Suwon , Gyeonggi-do 16419 , Republic of Korea
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50
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Chiribella G, Kristjánsson H. Quantum Shannon theory with superpositions of trajectories. Proc Math Phys Eng Sci 2019; 475:20180903. [PMID: 31236050 PMCID: PMC6545039 DOI: 10.1098/rspa.2018.0903] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2018] [Accepted: 03/29/2019] [Indexed: 11/12/2022] Open
Abstract
Shannon's theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon theory has focused on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantization where both the information and its propagation in space-time is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.
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Affiliation(s)
- Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, People's Republic of China
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, UK
| | - Hlér Kristjánsson
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, UK
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