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Jiráková K, Černoch A, Barasiński A, Lemr K. Enhancing collective entanglement witnesses through correlation with state purity. Sci Rep 2024; 14:16374. [PMID: 39013996 PMCID: PMC11252302 DOI: 10.1038/s41598-024-65385-7] [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: 04/25/2024] [Accepted: 06/19/2024] [Indexed: 07/18/2024] Open
Abstract
This research analyzes the adverse impact of white noise on collective quantum measurements and argues that such noise poses a significant obstacle for the otherwise straightforward deployment of collective measurements in quantum communications. Our findings then suggests addressing this issue by correlating outcomes of these measurements with quantum state purity. To test the concept, a support vector machine is employed to boost the performance of several collective entanglement witnesses by incorporating state purity into the classification task of distinguishing entangled states from separable ones. Furthermore, the application of machine learning allows to optimize specificity of entanglement detection given a target value of sensitivity. A response operating characteristic curve is reconstructed based on this optimization and the area under curve calculated to assess the efficacy of the proposed model. Finally, we test the presented approach on an experimental dataset of Werner states.
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Affiliation(s)
- Kateřina Jiráková
- Institute of Physics of the Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics AS CR, 17. listopadu 50a, 772 07, Olomouc, Czech Republic
| | - Antonín Černoch
- Institute of Physics of the Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics AS CR, 17. listopadu 50a, 772 07, Olomouc, Czech Republic
| | - Artur Barasiński
- Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204, Wroclaw, Poland
| | - Karel Lemr
- Joint Laboratory of Optics of Palacký University, Institute of Physics AS CR, Faculty of Science, Palacký University in Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
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Bartkiewicz K, Tulewicz P, Roik J, Lemr K. Synergic quantum generative machine learning. Sci Rep 2023; 13:12893. [PMID: 37558715 PMCID: PMC10412646 DOI: 10.1038/s41598-023-40137-1] [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: 02/11/2023] [Accepted: 08/05/2023] [Indexed: 08/11/2023] Open
Abstract
We introduce a new approach towards generative quantum machine learning significantly reducing the number of hyperparameters and report on a proof-of-principle experiment demonstrating our approach. Our proposal depends on collaboration between the generators and discriminator, thus, we call it quantum synergic generative learning. We present numerical evidence that the synergic approach, in some cases, compares favorably to recently proposed quantum generative adversarial learning. In addition to the results obtained with quantum simulators, we also present experimental results obtained with an actual programmable quantum computer. We investigate how a quantum computer implementing generative learning algorithm could learn the concept of a maximally-entangled state. After completing the learning process, the network is able both to recognize and to generate an entangled state. Our approach can be treated as one possible preliminary step to understanding how the concept of quantum entanglement can be learned and demonstrated by a quantum computer.
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Affiliation(s)
- Karol Bartkiewicz
- Institute of Spintronics and Quantum Information, Adam Mickiewicz University, 61-614, Poznan, Poland
- Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17, Listopadu 12, 771 46, Olomouc, Czech Republic
| | - Patrycja Tulewicz
- Institute of Spintronics and Quantum Information, Adam Mickiewicz University, 61-614, Poznan, Poland.
- Poznan Supercomputing and Networking Center, Institute of Bioorganic Chemistry of the Polish Academy of Sciences, 61-704, Poznan, Poland.
| | - Jan Roik
- Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17, Listopadu 12, 771 46, Olomouc, Czech Republic
| | - Karel Lemr
- Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17, Listopadu 12, 771 46, Olomouc, Czech Republic
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Laha A, Kumar S. Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance. Phys Rev E 2023; 107:034206. [PMID: 37073067 DOI: 10.1103/physreve.107.034206] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 02/07/2023] [Indexed: 04/20/2023]
Abstract
One of the key issues in problems related to quantum information theory is concerned with the distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also relates to fidelity, which is another quantity of immense importance in quantum information theory. In this work we derive exact results for the average fidelity and variance of the squared Bures distance between a fixed density matrix and a random density matrix and also between two independent random density matrices. These results go beyond the recently obtained results for the mean root fidelity and mean of the squared Bures distance. The availability of both mean and variance also enables us to provide a gamma-distribution-based approximation for the probability density of the squared Bures distance. The analytical results are corroborated using Monte Carlo simulations. Furthermore, we compare our analytical results with the mean and variance of the squared Bures distance between reduced density matrices generated using coupled kicked tops and a correlated spin chain system in a random magnetic field. In both cases, we find good agreement.
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Affiliation(s)
- Aritra Laha
- Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh 201314, India
| | - Santosh Kumar
- Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh 201314, India
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Burke PC, Nakerst G, Haque M. Assigning temperatures to eigenstates. Phys Rev E 2023; 107:024102. [PMID: 36932575 DOI: 10.1103/physreve.107.024102] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Accepted: 01/17/2023] [Indexed: 06/18/2023]
Abstract
In the study of thermalization in finite isolated quantum systems, an inescapable issue is the definition of temperature. We examine and compare different possible ways of assigning temperatures to energies or equivalently to eigenstates in such systems. A commonly used assignment of temperature in the context of thermalization is based on the canonical energy-temperature relationship, which depends only on energy eigenvalues and not on the structure of eigenstates. For eigenstates, we consider defining temperature by minimizing the distance between (full or reduced) eigenstate density matrices and canonical density matrices. We show that for full eigenstates, the minimizing temperature depends on the distance measure chosen and matches the canonical temperature for the trace distance; however, the two matrices are not close. With reduced density matrices, the minimizing temperature has fluctuations that scale with subsystem and system size but appears to be independent of distance measure. In particular limits, the two matrices become equivalent while the temperature tends to the canonical temperature.
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Affiliation(s)
- Phillip C Burke
- Department of Theoretical Physics, Maynooth University, Maynooth, Kildare, Ireland
| | - Goran Nakerst
- Department of Theoretical Physics, Maynooth University, Maynooth, Kildare, Ireland
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Masudul Haque
- Department of Theoretical Physics, Maynooth University, Maynooth, Kildare, Ireland
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
- Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany
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Bartkiewicz K, Gneiting C, Černoch A, Jiráková K, Lemr K, Nori F. Experimental kernel-based quantum machine learning in finite feature space. Sci Rep 2020; 10:12356. [PMID: 32704032 PMCID: PMC7378258 DOI: 10.1038/s41598-020-68911-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2020] [Accepted: 06/24/2020] [Indexed: 11/10/2022] Open
Abstract
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels' ability to separate points, i.e., their "resolution," under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.
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Affiliation(s)
- Karol Bartkiewicz
- Faculty of Physics, Adam Mickiewicz University, 61-614, Poznan, Poland.
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
| | - Clemens Gneiting
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, 351-0198, Japan
| | - Antonín Černoch
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
| | - Kateřina Jiráková
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46, Olomouc, Czech Republic
| | - Karel Lemr
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, 351-0198, Japan
- Department of Physics, The University of Michigan, Ann Arbor, MI, 48109-1040, USA
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