Distributed quantum algorithm for Simon's problem

• URL: http://arxiv.org/abs/2204.11388v4
• Date: Fri, 6 May 2022 16:03:58 GMT
• Title: Distributed quantum algorithm for Simon's problem
• Authors: Jiawei Tan, Ligang Xiao, Daowen Qiu, Le Luo, Paulo Mateus
• Abstract summary: We study the Simon's problem in distributed scenarios and design a distributed quantum algorithm to solve the problem. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits.
• Score: 2.26741603346646
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we study the Simon's problem in distributed scenarios and design a distributed quantum algorithm to solve the problem. The algorithm proposed by us has the advantage of exponential acceleration compared with the classical distributed computing, and has the advantage of square acceleration compared with the best distributed quantum algorithm proposed before. In particular, the previous distributed quantum algorithm for Simon's problem can not be extended to the case of more than {\it two computing nodes} (i.e. two subproblems), but our distributed quantum algorithm can be extended to the case of {\it multiple computing nodes} (i.e. multiple subproblems) as well.

Related papers

• 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)
• Variational Quantum Algorithms for the Allocation of Resources in a Cloud/Edge Architecture [1.072460284847973]
  We show that Variational Quantum Algorithms can be a viable alternative to classical algorithms in the near future. In particular, we compare the performances, in terms of success probability, of two algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) The simulation experiments, performed for a set of simple problems, %CM230124 that involve a Cloud and two Edge nodes, show that the VQE algorithm ensures better performances when it is equipped with appropriate circuit textitansatzes that are able to restrict the search space
  arXiv  Detail & Related papers  (2024-01-25T17:37:40Z)
• Exact distributed quantum algorithm for generalized Simon's problem [8.061563029894927]
  Simon's problem is one of the most important problems demonstrating the power of quantum algorithms. We introduce a corresponding distributed quantum algorithm for Simon's problem. We refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique.
  arXiv  Detail & Related papers  (2023-07-26T17:25:39Z)
• Making the cut: two methods for breaking down a quantum algorithm [0.0]
  It remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy, small-scale quantum hardware. We identify and characterize two methods of breaking down'' quantum algorithms into rounds of lower (query) depth. We show that for the first problem parallelization offers the best performance, while for the second is the better choice.
  arXiv  Detail & Related papers  (2023-05-17T18:00:06Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• 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)
• 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)
• Quantum algorithm for stochastic optimal stopping problems with applications in finance [60.54699116238087]
  The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in optimal stopping theory. We propose a quantum LSM based on quantum access to a process, on quantum circuits for computing the optimal stopping times, and on quantum techniques for Monte Carlo.
  arXiv  Detail & Related papers  (2021-11-30T12:21:41Z)
• 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)
• Quantum advantage and noise reduction in distributed quantum computing [0.0]
  Distributed quantum computing can give substantial noise reduction due to shallower circuits. We show that the distributed Simon algorithm retains the exponential advantage, but the complexity deteriorates. The distributed Deutsch-Jozsa deteriorates to being probabilistic but retains a quantum advantage over classical random sampling.
  arXiv  Detail & Related papers  (2021-04-15T23:27:39Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

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.