Quantum mean value approximator for hard integer value problems

• URL: http://arxiv.org/abs/2105.13106v1
• Date: Thu, 27 May 2021 13:03:52 GMT
• Title: Quantum mean value approximator for hard integer value problems
• Authors: David Joseph, Antonio J. Martinez, Cong Ling, Florian Mintert
• Abstract summary: We show that an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems.
• Score: 19.4417702222583
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum eigensolvers. We show that such an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems, such as the shortest vector problem (SVP) investigated in this work.

Related papers

• Quantum Approximate Optimisation for Not-All-Equal SAT [9.427635404752936]
  We apply variational quantum algorithm QAOA to a variant of satisfiability problem (SAT): Not-All-Equal SAT. We show that while the runtime of both solvers scales exponentially with the problem size, the scaling for QAOA is smaller for large enough circuit depths.
  arXiv  Detail & Related papers  (2024-01-05T15:11:24Z)
• Efficient DCQO Algorithm within the Impulse Regime for Portfolio Optimization [41.94295877935867]
  We propose a faster digital quantum algorithm for portfolio optimization using the digitized-counterdiabatic quantum optimization (DCQO) paradigm. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We experimentally demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer.
  arXiv  Detail & Related papers  (2023-08-29T17:53:08Z)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• 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)
• Stochastic optimization algorithms for quantum applications [0.0]
  We review the use of first-order, second-order, and quantum natural gradient optimization methods, and propose new algorithms defined in the field of complex numbers. The performance of all methods is evaluated by means of their application to variational quantum eigensolver, quantum control of quantum states, and quantum state estimation.
  arXiv  Detail & Related papers  (2022-03-11T16:17:05Z)
• Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits [15.279642278652654]
  We present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
  arXiv  Detail & Related papers  (2021-12-21T12:41:31Z)
• Efficiently Solve the Max-cut Problem via a Quantum Qubit Rotation Algorithm [7.581898299650999]
  We introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA) The approximate solution of the max-cut problem can be obtained with probability close to 1. We compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.
  arXiv  Detail & Related papers  (2021-10-15T11:19:48Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Filtering variational quantum algorithms for combinatorial optimization [0.0]
  We introduce the Variational Quantum Eigensolver (F-VQE) which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. We also explore the use of causal cones to reduce the number of qubits required on a quantum computer.
  arXiv  Detail & Related papers  (2021-06-18T11:07:33Z)
• 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.