Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens

• URL: http://arxiv.org/abs/2306.09444v2
• Date: Sat, 9 Dec 2023 19:07:45 GMT
• Title: Large-Scale Quantum Separability Through a Reproducible Machine Learning Lens
• Authors: Balthazar Casal\'e, Giuseppe Di Molfetta, Sandrine Anthoine, Hachem Kadri
• Abstract summary: The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. We propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios.
• Score: 5.499796332553708
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in large-scale scenarios. We provide an efficient Frank-Wolfe-based algorithm to approximately seek the nearest separable density matrix and derive a systematic way for labeling density matrices as separable or entangled, allowing us to treat quantum separability as a classification problem. Our method is applicable to any two-qudit mixed states. Numerical experiments with quantum states of 3- and 7-dimensional qudits validate the efficiency of the proposed procedure, and demonstrate that it scales up to thousands of density matrices with a high quantum entanglement detection accuracy. This takes a step towards benchmarking quantum separability to support the development of more powerful entanglement detection techniques.

Related papers

• Machine Learning approach to reconstruct Density Matrices from Quantum Marginals [0.0]
  We propose a machine learning approach to address one aspect of the quantum marginal problem. Our method involves combining a quantum marginal imposition technique with convolutional denoising autoencoders.
  arXiv  Detail & Related papers  (2024-10-15T00:00:27Z)
• A Quantum Approximate Optimization Method For Finding Hadamard Matrices [0.0]
  We propose a novel qubit-efficient method by implementing the Hadamard matrix searching algorithm on a gate-based quantum computer. We present the formulation of the method, construction of corresponding quantum circuits, and experiment results in both a quantum simulator and a real gate-based quantum computer.
  arXiv  Detail & Related papers  (2024-08-15T06:25:50Z)
• Quantum State Preparation for Probability Distributions with Mirror Symmetry Using Matrix Product States [0.0]
  Quantum circuits for loading probability distributions into quantum states are essential subroutines in quantum algorithms used in physics, finance engineering, and machine learning. We propose a novel quantum state preparation method for probability distribution with mirror symmetry using matrix product states. Our method reduces the entanglement of probability distributions and improves the accuracy of approximations by matrix product states.
  arXiv  Detail & Related papers  (2024-03-25T13:03:35Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Squeezing and quantum approximate optimization [0.6562256987706128]
  Variational quantum algorithms offer fascinating prospects for the solution of optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations therein remain unclear. We show numerically as well as on an IBM quantum chip how highly squeezed states are generated in a systematic procedure.
  arXiv  Detail & Related papers  (2022-05-20T18:00:06Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays [39.76254807200083]
  We experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We find the problem hardness is controlled by the solution degeneracy and number of local minima. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions.
  arXiv  Detail & Related papers  (2022-02-18T19:00:01Z)
• Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers [0.0]
  A novel hybrid quantum-classical algorithm is presented for the solution of the quantum-chemical ground-state energy problem. The new approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits.
  arXiv  Detail & Related papers  (2022-02-04T22:28:17Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.