Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck

• URL: http://arxiv.org/abs/2311.11188v2
• Date: Fri, 12 Jan 2024 05:31:16 GMT
• Title: Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck
• Authors: Masahito Hayashi and Geng Liu
• Abstract summary: We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. We apply our algorithm to the quantum information bottleneck with three quantum systems. Our numerical analysis shows that our algorithm is better than their algorithm.
• Score: 55.22418739014892
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. (IEEE Trans. IT, 67, 946 (2021)) to a function defined over a set of density matrices with linear constraints so that our algorithm can be applied to optimizations of quantum operations. This algorithm has wider applicability. Hence, we apply our algorithm to the quantum information bottleneck with three quantum systems, which can be used for quantum learning. We numerically compare our obtained algorithm with the existing algorithm by Grimsmo and Still (Phys. Rev. A, 94, 012338 (2016)). Our numerical analysis shows that our algorithm is better than their algorithm.

Related papers

• Quantum multi-row iteration algorithm for linear systems with non-square coefficient matrices [7.174256268278207]
  We propose a quantum algorithm inspired by the classical multi-row iteration method. Our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems.
  arXiv  Detail & Related papers  (2024-09-06T03:32:02Z)
• The Algorithm for Solving Quantum Linear Systems of Equations With Coherent Superposition and Its Extended Applications [8.8400072344375]
  We propose two quantum algorithms for solving quantum linear systems of equations with coherent superposition. The two quantum algorithms can both compute the rank and general solution by one measurement. Our analysis indicates that the proposed algorithms are mainly suitable for conducting attacks against lightweight symmetric ciphers.
  arXiv  Detail & Related papers  (2024-05-11T03:03:14Z)
• Quantum algorithms for Hopcroft's problem [45.45456673484445]
  We study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. The classical complexity of this problem is well-studied, with the best known algorithm running in $O(n4/3)$ time. Our results are two different quantum algorithms with time complexity $widetilde O(n5/6)$.
  arXiv  Detail & Related papers  (2024-05-02T10:29:06Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Polynomial-depth quantum algorithm for computing matrix determinant [46.13392585104221]
  We propose an algorithm for calculating the determinant of a square matrix, and construct a quantum circuit realizing it. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems.
  arXiv  Detail & Related papers  (2024-01-29T23:23:27Z)
• Iterative Quantum Algorithms for Maximum Independent Set: A Tale of Low-Depth Quantum Algorithms [0.0]
  We study a new class of hybrid approaches to quantum optimization, termed Iterative Maximum Quantum Algorithms. We show that for QAOA with depth $p=1$, this algorithm performs exactly the same operations and selections as the classical greedy algorithm for MIS.
  arXiv  Detail & Related papers  (2023-09-22T18:00:03Z)
• Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems [0.2624902795082451]
  We investigate the limitations of quantum computers for solving nonlinear dynamical systems. We provide a significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector.
  arXiv  Detail & Related papers  (2023-07-13T11:06:02Z)
• Simulating the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm with limited entanglement using tensor-networks [0.0]
  We simulate the execution of quantum algorithms with limited entanglement. We find that the algorithms can be executed with high fidelity even if the entanglement is somewhat reduced. Our results are promising for the execution of these algorithms on future quantum computers.
  arXiv  Detail & Related papers  (2023-04-04T12:42:18Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)

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.