Quantum Optimization Heuristics with an Application to Knapsack Problems

• URL: http://arxiv.org/abs/2108.08805v3
• Date: Thu, 3 Feb 2022 20:49:58 GMT
• Title: Quantum Optimization Heuristics with an Application to Knapsack Problems
• Authors: Wim van Dam, Karim Eldefrawy, Nicholas Genise, Natalie Parham
• Abstract summary: This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions.
• Score: 5.866941279460248
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions. To analyze the benefits of these two techniques we run the quantum algorithm on known hard instances of the Knapsack Problem using unit depth quantum circuits. The results show that the adjusted quantum optimization heuristics typically perform better than various classical heuristics.

Related papers

• Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems [65.268245109828]
  We compare the performance of classicals across a series of partially-randomized tasks. We focus on local zeroth-orders due to their generally favorable performance and query-efficiency on quantum systems.
  arXiv  Detail & Related papers  (2023-10-14T02:13:26Z)
• 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)
• 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)
• A quantum advantage over classical for local max cut [48.02822142773719]
  Quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. Results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical.
  arXiv  Detail & Related papers  (2023-04-17T16:42:05Z)
• Quantum-Enhanced Greedy Combinatorial Optimization Solver [12.454028945013924]
  We introduce an iterative quantum optimization algorithm to solve optimization problems. We implement the quantum algorithm on a programmable superconducting quantum system using up to 72 qubits. We find the quantum algorithm systematically outperforms its classical greedy counterpart, signaling a quantum enhancement.
  arXiv  Detail & Related papers  (2023-03-09T18:59:37Z)
• 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)
• 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)
• Quantum mean value approximator for hard integer value problems [19.4417702222583]
  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.
  arXiv  Detail & Related papers  (2021-05-27T13:03:52Z)
• Optimization of the Variational Quantum Eigensolver for Quantum Chemistry Applications [0.0]
  The variational quantum eigensolver algorithm is designed to determine the ground state of a quantum mechanical system. We study methods of reducing the number of required qubit manipulations, prone to induce errors, for the variational quantum eigensolver.
  arXiv  Detail & Related papers  (2021-02-02T22:20:12Z)
• Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms [0.0]
  We apply the divide-and-conquer approach to reduce the original problem to a collection of smaller problems. This technique can be applied to any QUBO instance and leads to either an all-classical or a hybrid quantum-classical approach.
  arXiv  Detail & Related papers  (2021-01-19T19:00:40Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

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.