1
|
Suprano A, Zia D, Innocenti L, Lorenzo S, Cimini V, Giordani T, Palmisano I, Polino E, Spagnolo N, Sciarrino F, Palma GM, Ferraro A, Paternostro M. Experimental Property Reconstruction in a Photonic Quantum Extreme Learning Machine. PHYSICAL REVIEW LETTERS 2024; 132:160802. [PMID: 38701482 DOI: 10.1103/physrevlett.132.160802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 03/07/2024] [Indexed: 05/05/2024]
Abstract
Recent developments have led to the possibility of embedding machine learning tools into experimental platforms to address key problems, including the characterization of the properties of quantum states. Leveraging on this, we implement a quantum extreme learning machine in a photonic platform to achieve resource-efficient and accurate characterization of the polarization state of a photon. The underlying reservoir dynamics through which such input state evolves is implemented using the coined quantum walk of high-dimensional photonic orbital angular momentum and performing projective measurements over a fixed basis. We demonstrate how the reconstruction of an unknown polarization state does not need a careful characterization of the measurement apparatus and is robust to experimental imperfections, thus representing a promising route for resource-economic state characterization.
Collapse
Affiliation(s)
- Alessia Suprano
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - Danilo Zia
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - Luca Innocenti
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy
| | - Salvatore Lorenzo
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy
| | - Valeria Cimini
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - Taira Giordani
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - Ivan Palmisano
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, BT7 1NN, United Kingdom
| | - Emanuele Polino
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
- Centre for Quantum Dynamics and Centre for Quantum Computation and Communication Technology, Griffith University, Yuggera Country, Brisbane, Queensland 4111, Australia
| | - Nicolò Spagnolo
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - Fabio Sciarrino
- Dipartimento di Fisica - Sapienza Università di Roma, Piazza le Aldo Moro 5, I-00185 Roma, Italy
| | - G Massimo Palma
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy
| | - Alessandro Ferraro
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, BT7 1NN, United Kingdom
- Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133 Milano, Italy
| | - Mauro Paternostro
- Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy
- Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen's University Belfast, BT7 1NN, United Kingdom
| |
Collapse
|
2
|
Ahmed S, Quijandría F, Kockum AF. Gradient-Descent Quantum Process Tomography by Learning Kraus Operators. PHYSICAL REVIEW LETTERS 2023; 130:150402. [PMID: 37115870 DOI: 10.1103/physrevlett.130.150402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Revised: 02/17/2023] [Accepted: 03/16/2023] [Indexed: 06/19/2023]
Abstract
We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems.
Collapse
Affiliation(s)
- Shahnawaz Ahmed
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Fernando Quijandría
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
- Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Anton Frisk Kockum
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| |
Collapse
|
3
|
Lohani S, Lukens J, Glasser RT, Searles TA, Kirby B. Data-Centric Machine Learning in Quantum Information Science. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac9036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
We propose a series of data-centric heuristics for improving the performance of machine learning systems when applied to problems in quantum information science. In particular, we consider how systematic engineering of training sets can significantly enhance the accuracy of pre-trained neural networks used for quantum state reconstruction without altering the underlying architecture. We find that it is not always optimal to engineer training sets to exactly match the expected distribution of a target scenario, and instead, performance can be further improved by biasing the training set to be slightly more mixed than the target. This is due to the heterogeneity in the number of free variables required to describe states of different purity, and as a result, overall accuracy of the network improves when training sets of a fixed size focus on states with the least constrained free variables. For further clarity, we also include a ``toy model'' demonstration of how spurious correlations can inadvertently enter synthetic data sets used for training, how the performance of systems trained with these correlations can degrade dramatically, and how the inclusion of even relatively few counterexamples can effectively remedy such problems.
Collapse
|
4
|
Direct Parameter Estimations from Machine Learning-Enhanced Quantum State Tomography. Symmetry (Basel) 2022. [DOI: 10.3390/sym14050874] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
With the power to find the best fit to arbitrarily complicated symmetry, machine-learning (ML)-enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with a large Hilbert space, but cab keep feature extractions with high precision, capturing the underlying symmetry in data. With the experimentally measured data generated from the balanced homodyne detectors, we compare the degradation information about quantum noise squeezed states predicted by the reconstruction and characteristic models; both are in agreement with the empirically fitting curves obtained from the covariance method. Such a ML-QST with direct parameter estimations illustrates a crucial diagnostic toolbox for applications with squeezed states, from quantum information process, quantum metrology, advanced gravitational wave detectors, to macroscopic quantum state generation.
Collapse
|
5
|
Hsieh HY, Chen YR, Wu HC, Chen HL, Ning J, Huang YC, Wu CM, Lee RK. Extract the Degradation Information in Squeezed States with Machine Learning. PHYSICAL REVIEW LETTERS 2022; 128:073604. [PMID: 35244420 DOI: 10.1103/physrevlett.128.073604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 12/18/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine-learning architecture with a convolutional neural network, we illustrate a fast, robust, and precise quantum state tomography for continuous variables, through the experimentally measured data generated from the balanced homodyne detectors. Compared with the maximum likelihood estimation method, which suffers from time-consuming and overfitting problems, a well-trained machine fed with squeezed vacuum and squeezed thermal states can complete the task of reconstruction of the density matrix in less than one second. Moreover, the resulting fidelity remains as high as 0.99 even when the antisqueezing level is higher than 20 dB. Compared with the phase noise and loss mechanisms coupled from the environment and surrounding vacuum, experimentally, the degradation information is unveiled with machine learning for low and high noisy scenarios, i.e., with the antisqueezing levels at 12 dB and 18 dB, respectively. Our neural network enhanced quantum state tomography provides the metrics to give physical descriptions of every feature observed in the quantum state with a single scan measurement just by varying the local oscillator phase from 0 to 2π and paves a way of exploring large-scale quantum systems in real time.
Collapse
Affiliation(s)
- Hsien-Yi Hsieh
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Yi-Ru Chen
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Hsun-Chung Wu
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Hua Li Chen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Jingyu Ning
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Yao-Chin Huang
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Chien-Ming Wu
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Ray-Kuang Lee
- Institute of Photonics Technologies, National Tsing Hua University, Hsinchu 30013, Taiwan
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
- Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan
- Center for Quantum Technology, Hsinchu 30013, Taiwan
| |
Collapse
|
6
|
Borah S, Sarma B, Kewming M, Milburn GJ, Twamley J. Measurement-Based Feedback Quantum Control with Deep Reinforcement Learning for a Double-Well Nonlinear Potential. PHYSICAL REVIEW LETTERS 2021; 127:190403. [PMID: 34797162 DOI: 10.1103/physrevlett.127.190403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 07/19/2021] [Accepted: 09/20/2021] [Indexed: 06/13/2023]
Abstract
Closed loop quantum control uses measurement to control the dynamics of a quantum system to achieve either a desired target state or target dynamics. In the case when the quantum Hamiltonian is quadratic in x and p, there are known optimal control techniques to drive the dynamics toward particular states, e.g., the ground state. However, for nonlinear Hamiltonian such control techniques often fail. We apply deep reinforcement learning (DRL), where an artificial neural agent explores and learns to control the quantum evolution of a highly nonlinear system (double well), driving the system toward the ground state with high fidelity. We consider a DRL strategy which is particularly motivated by experiment where the quantum system is continuously but weakly measured. This measurement is then fed back to the neural agent and used for training. We show that the DRL can effectively learn counterintuitive strategies to cool the system to a nearly pure "cat" state, which has a high overlap fidelity with the true ground state.
Collapse
Affiliation(s)
- Sangkha Borah
- Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Bijita Sarma
- Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Michael Kewming
- Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland, 4072 Australia
| | - Gerard J Milburn
- Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland, 4072 Australia
| | - Jason Twamley
- Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| |
Collapse
|
7
|
Ahmed S, Sánchez Muñoz C, Nori F, Kockum AF. Quantum State Tomography with Conditional Generative Adversarial Networks. PHYSICAL REVIEW LETTERS 2021; 127:140502. [PMID: 34652197 DOI: 10.1103/physrevlett.127.140502] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Revised: 05/21/2021] [Accepted: 06/10/2021] [Indexed: 06/13/2023]
Abstract
Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.
Collapse
Affiliation(s)
- Shahnawaz Ahmed
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| | - Carlos Sánchez Muñoz
- Departamento de Fisica Teorica de la Materia Condensada and Condensed Matter Physics Center (IFIMAC), Universidad Autonoma de Madrid, Madrid 28049, Spain
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Anton Frisk Kockum
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden
| |
Collapse
|
8
|
Danaci O, Lohani S, Kirby BT, Glasser RT. Machine learning pipeline for quantum state estimation with incomplete measurements. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abe5f5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.
Collapse
|
9
|
Herrera M, Peterson JPS, Serra RM, D'Amico I. Easy Access to Energy Fluctuations in Nonequilibrium Quantum Many-Body Systems. PHYSICAL REVIEW LETTERS 2021; 127:030602. [PMID: 34328771 DOI: 10.1103/physrevlett.127.030602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We combine theoretical and experimental efforts to propose a method for studying energy fluctuations, in particular, to obtain the related bistochastic matrix of transition probabilities by means of simple measurements at the end of a protocol that drives a many-body quantum system out of equilibrium. This scheme is integrated with numerical optimizations in order to ensure a proper analysis of the experimental data, leading to physical probabilities. The method is experimentally evaluated employing a two interacting spin-1/2 system in a nuclear magnetic resonance setup. We show how to recover the transition probabilities using only local measures, which enables an experimental verification of the detailed fluctuation theorem in a many-body system driven out of equilibrium.
Collapse
Affiliation(s)
- Marcela Herrera
- Departamento de Ciencias Naturales, Universidad Autónoma de Occidente, 760030 Cali, Colombia
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - John P S Peterson
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
| | - Roberto M Serra
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Irene D'Amico
- Department of Physics, University of York, York YO10 5DD, United Kingdom
| |
Collapse
|