求解0-1背包问题的量子算法

IF 8.3 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Sören Wilkening, Andreea-Iulia Lefterovici, Lennart Binkowski, Michael Perk, Sándor P. Fekete, Tobias J. Osborne
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引用次数: 0

摘要

我们提出了两个新的贡献实现和评估量子优势在解决困难的优化问题,在理论上和可预见的实践。(1)引入“量子树生成器”,叠加生成给定0-1背包实例的所有可行解;结合振幅放大,这确定了最优解。假设完全连接的逻辑量子位和可比较的量子时钟速度,QTG提供了与只有100个变量的实例的经典最先进的背包求解器竞争的运行时视角。(2)通过引入一种利用经典求解器的测井数据的新技术,我们可以预测我们的方法的运行时间,远远超出现有量子平台和模拟器的范围,对于多达600个变量的基准实例。在给定的假设下,我们证明了QTG在这种情况下的潜在实用量子优势,表明了一种解决难组合优化问题的有效方法的前景。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A quantum algorithm for solving 0-1 Knapsack problems

A quantum algorithm for solving 0-1 Knapsack problems

We present two novel contributions for achieving and assessing quantum advantage in solving difficult optimisation problems, both in theory and foreseeable practice. (1) We introduce the “Quantum Tree Generator” to generate in superposition all feasible solutions of a given 0-1 knapsack instance; combined with amplitude amplification, this identifies optimal solutions. Assuming fully connected logical qubits and comparable quantum clock speed, QTG offers perspectives for runtimes competitive to classical state-of-the-art knapsack solvers for instances with only 100 variables. (2) By introducing a new technique that exploits logging data from a classical solver, we can predict the runtime of our method way beyond the range of existing quantum platforms and simulators, for benchmark instances with up to 600 variables. Under the given assumptions, we demonstrate the QTG’s potential practical quantum advantage for such instances, indicating the promise of an effective approach for hard combinatorial optimisation problems.

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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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