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Chiesa A, Santini P, Garlatti E, Luis F, Carretta S. Molecular nanomagnets: a viable path toward quantum information processing? REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:034501. [PMID: 38314645 DOI: 10.1088/1361-6633/ad1f81] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 01/17/2024] [Indexed: 02/06/2024]
Abstract
Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.
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Affiliation(s)
- A Chiesa
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - P Santini
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - E Garlatti
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - F Luis
- Instituto de Nanociencia y Materiales de Aragon (INMA), CSIC, Universidad de Zaragoza, Zaragoza, Spain
- Departamento de Fısica de la Materia Condensada, Universidad de Zaragoza, Zaragoza, Spain
| | - S Carretta
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
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2
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DeBry K, Sinanan-Singh J, Bruzewicz CD, Reens D, Kim ME, Roychowdhury MP, McConnell R, Chuang IL, Chiaverini J. Experimental Quantum Channel Discrimination Using Metastable States of a Trapped Ion. PHYSICAL REVIEW LETTERS 2023; 131:170602. [PMID: 37955505 DOI: 10.1103/physrevlett.131.170602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 08/17/2023] [Indexed: 11/14/2023]
Abstract
We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped ^{40}Ca^{+} ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the six-dimensional D_{5/2} state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding 99% in each case, limited entirely by known experimental imperfections.
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Affiliation(s)
- Kyle DeBry
- Department of Physics, Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - Jasmine Sinanan-Singh
- Department of Physics, Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Colin D Bruzewicz
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - David Reens
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - May E Kim
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - Matthew P Roychowdhury
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - Robert McConnell
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
| | - Isaac L Chuang
- Department of Physics, Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - John Chiaverini
- Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02421, USA
- Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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3
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Zache TV, González-Cuadra D, Zoller P. Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories. PHYSICAL REVIEW LETTERS 2023; 131:171902. [PMID: 37955498 DOI: 10.1103/physrevlett.131.171902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Revised: 08/10/2023] [Accepted: 09/25/2023] [Indexed: 11/14/2023]
Abstract
Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.
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Affiliation(s)
- Torsten V Zache
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Daniel González-Cuadra
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria
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4
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Davoudi Z, Mueller N, Powers C. Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States. PHYSICAL REVIEW LETTERS 2023; 131:081901. [PMID: 37683176 DOI: 10.1103/physrevlett.131.081901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 02/27/2023] [Accepted: 06/01/2023] [Indexed: 09/10/2023]
Abstract
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
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Affiliation(s)
- Zohreh Davoudi
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Niklas Mueller
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Connor Powers
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
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Das S, Caruso F. A hybrid-qudit representation of digital RGB images. Sci Rep 2023; 13:13671. [PMID: 37608205 PMCID: PMC10444894 DOI: 10.1038/s41598-023-39906-9] [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: 03/24/2023] [Accepted: 08/01/2023] [Indexed: 08/24/2023] Open
Abstract
Quantum image processing is an emerging topic in the field of quantum information and technology. In this paper, we propose a new quantum image representation of RGB images with deterministic image retrieval, which is an improvement over all the similar existing representations in terms of using minimum resource. We use two entangled quantum registers constituting of total 7 qutrits to encode the color channels and their intensities. Additionally, we generalize the existing encoding methods by using both qubits and qutrits to encode the pixel positions of a rectangular image. This hybrid-qudit approach aligns well with the current progress of NISQ devices in incorporating higher dimensional quantum systems than qubits. We then describe the image encoding method using higher-order qubit-qutrit gates, and demonstrate the decomposition of these gates in terms of simpler elementary gates. We use the Google Cirq's quantum simulator to verify the image preparation in both the ideal noise-free scenario and in presence of realistic noise modelling. We show that the complexity of the image encoding process is linear in the number of pixels. Lastly, we discuss the image compression and some basic RGB image processing protocols using our representation.
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Affiliation(s)
- Sreetama Das
- Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Italy.
- European Laboratory for Non-Linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Italy.
| | - Filippo Caruso
- Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Italy
- European Laboratory for Non-Linear Spectroscopy (LENS), University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Italy
- QSTAR and CNR-INO, Largo Enrico Fermi 2, 50125, Firenze, Italy
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Yin XF, Yao XC, Wu B, Fei YY, Mao Y, Zhang R, Liu LZ, Wang Z, Li L, Liu NL, Wilczek F, Chen YA, Pan JW. Solving independent set problems with photonic quantum circuits. Proc Natl Acad Sci U S A 2023; 120:e2212323120. [PMID: 37216545 PMCID: PMC10235971 DOI: 10.1073/pnas.2212323120] [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: 08/08/2022] [Accepted: 03/01/2023] [Indexed: 05/24/2023] Open
Abstract
An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.
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Affiliation(s)
- Xu-Fei Yin
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Xing-Can Yao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Biao Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing100871, China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai200240, China
| | - Yue-Yang Fei
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Yingqiu Mao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Rui Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Li-Zheng Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Zhenduo Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing100871, China
| | - Li Li
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Nai-Le Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Frank Wilczek
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai200240, China
- Center for Theoretical Physics, MIT, Cambridge, MA02139
- T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai200240, China
- Department of Physics, Stockholm University, StockholmSE-106 91, Sweden
- Department of Physics and Origins Project, Arizona State University, Tempe, AZ25287
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
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7
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Yan Z, Wang YC, Samajdar R, Sachdev S, Meng ZY. Emergent Glassy Behavior in a Kagome Rydberg Atom Array. PHYSICAL REVIEW LETTERS 2023; 130:206501. [PMID: 37267547 DOI: 10.1103/physrevlett.130.206501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 03/12/2023] [Accepted: 03/16/2023] [Indexed: 06/04/2023]
Abstract
We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.
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Affiliation(s)
- Zheng Yan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Yan-Cheng Wang
- Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310023, China
- Zhongfa Aviation Institute of Beihang University, Hangzhou 310023, China
| | - Rhine Samajdar
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
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Hrmo P, Wilhelm B, Gerster L, van Mourik MW, Huber M, Blatt R, Schindler P, Monz T, Ringbauer M. Native qudit entanglement in a trapped ion quantum processor. Nat Commun 2023; 14:2242. [PMID: 37076475 PMCID: PMC10115791 DOI: 10.1038/s41467-023-37375-2] [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: 01/18/2023] [Accepted: 03/15/2023] [Indexed: 04/21/2023] Open
Abstract
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.
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Affiliation(s)
- Pavel Hrmo
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria.
| | - Benjamin Wilhelm
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Lukas Gerster
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Martin W van Mourik
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Marcus Huber
- Atominstitut, Technische Universität Wien, 1020, Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria
| | - Rainer Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Philipp Schindler
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Thomas Monz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Martin Ringbauer
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
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9
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Nikolaeva AS, Kiktenko EO, Fedorov AK. Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover's Algorithm with Qudits. ENTROPY (BASEL, SWITZERLAND) 2023; 25:387. [PMID: 36832752 PMCID: PMC9955871 DOI: 10.3390/e25020387] [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: 01/26/2023] [Revised: 02/14/2023] [Accepted: 02/15/2023] [Indexed: 06/18/2023]
Abstract
Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states-qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems-so-called ququints-that use ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.
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Affiliation(s)
- Anstasiia S. Nikolaeva
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
| | - Evgeniy O. Kiktenko
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
| | - Aleksey K. Fedorov
- Russian Quantum Center, Skolkovo, Moscow 121205, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
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10
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Samajdar R, Joshi DG, Teng Y, Sachdev S. Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays. PHYSICAL REVIEW LETTERS 2023; 130:043601. [PMID: 36763444 DOI: 10.1103/physrevlett.130.043601] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 12/05/2022] [Indexed: 06/18/2023]
Abstract
Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.
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Affiliation(s)
- Rhine Samajdar
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Princeton University, Princeton, New Jersey, 08544, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey, 08544, USA
| | - Darshan G Joshi
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Yanting Teng
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
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11
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Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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