Quantum optimization algorithm based on multistep quantum computation

• URL: http://arxiv.org/abs/2306.17363v1
• Date: Fri, 30 Jun 2023 01:58:23 GMT
• Title: Quantum optimization algorithm based on multistep quantum computation
• Authors: Hefeng Wang, Hua Xiang
• Abstract summary: We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation. In this algorithm, the dimension of the search space of the problem can be reduced exponentially step by step. We have tested the algorithm for some continuous test functions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the state space of the problem. Usually the cost for solving the problem increases dramatically with the size of the problem. In this algorithm, the dimension of the search space of the problem can be reduced exponentially step by step. We construct a sequence of Hamiltonians such that the search space of a Hamiltonian is nested in that of the previous one. By applying a multistep quantum computation process, the optimal vector is finally located in a small state space and can be determined efficiently. One of the most difficult problems in optimization is that a trial vector is trapped in a deep local minimum while the global minimum is missed, this problem can be alleviated in our algorithm and the runtime is proportional to the number of the steps of the algorithm, provided certain conditions are satisfied. We have tested the algorithm for some continuous test functions.

Related papers

• Space-Efficient Quantum Error Reduction without log Factors [50.10645865330582]
  We present a new highly simplified construction of a purifier, that can be understood as a weighted walk on a line similar to a random walk interpretation of majority voting. Our purifier has exponentially better space complexity than the previous one, and quadratically better dependence on the soundness-completeness gap of the algorithm being purified.
  arXiv  Detail & Related papers  (2025-02-13T12:04:39Z)
• A quantum speedup algorithm for TSP based on quantum dynamic programming with very few qubits [0.0]
  We propose a quantum algorithm to generate the uniform superposition state of all N-length Hamiltonian cycles as an initial state within gate complexity. Compared to some algorithms that theoretically have lower query complexities but lack practical implementation solutions, our algorithm has feasible circuit implementation.
  arXiv  Detail & Related papers  (2025-02-12T23:58:25Z)
• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Solving The Travelling Salesman Problem Using A Single Qubit [0.0]
  The travelling salesman problem (TSP) is a popular NP-hard-combinatorial optimization problem. We present an algorithm that solves an arbitrary TSP using a single qubit by invoking the principle of quantum parallelism. The underlying framework of our algorithm is a quantum version of the classical Brachistochrone approach.
  arXiv  Detail & Related papers  (2024-07-24T12:06:37Z)
• 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)
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck [55.22418739014892]
  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.
  arXiv  Detail & Related papers  (2023-11-19T00:06:11Z)
• Efficient Quantum Algorithms for Quantum Optimal Control [2.9370710299422607]
  We present efficient quantum algorithms for solving the quantum optimal control problem. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. Our quantum algorithms require fault-tolerant quantum computers.
  arXiv  Detail & Related papers  (2023-04-05T17:33:57Z)
• Quantum speedup of leverage score sampling and its application [0.0]
  In this paper, we propose a quantum algorithm to accelerate the computation of leverage scores. As an application, we propose a new quantum algorithm for rigid regression problems with vector solution outputs.
  arXiv  Detail & Related papers  (2023-01-15T14:40:18Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• 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)
• Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits [99.70167985955352]
  We study the problem of zero-order optimization of a strongly convex function. We consider a randomized approximation of the projected gradient descent algorithm. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters.
  arXiv  Detail & Related papers  (2020-06-14T10:42:23Z)

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.