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arXiv 2301.06978quant-ph
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在量子计算机上以指数级减少的量子比特数求解多种NP难问题

Solving various NP-Hard problems using exponentially fewer qubits on a Quantum Computer

Yagnik Chatterjee, Eric Bourreau, Marko J. Rančić

AI总结:

本文提出一种随问题规模对数级扩展的量子优化方法,在NISQ设备上以指数级减少的量子比特数求解最大割、最大团等NP难问题,将可处理图规模提升近十倍。

摘要:

NP难问题通常被认为无法通过一般的多项式时间算法精确求解。过去几年中,用于处理此类组合问题的混合量子-经典算法引起了极大关注。这类算法本质上是启发式的,旨在获得近似解。在这方面,量子计算的主要承诺之一是显著缩短计算时间和/或具备处理大规模问题的能力。然而,硬件仍处于起步阶段,当前的含噪声中等规模量子(NISQ)计算机尚无法优化具有工业现实意义的问题。此外,量子比特的存储和纠缠的引入需要极端的物理条件。像QAOA这样的量子优化算法存在一个问题,即其规模随问题规模线性增长。本文基于一种专有方法进行构建,该方法随问题规模呈对数级扩展,从而为在基于门的量子计算机上处理前所未有规模的优化问题开辟了途径。为了测试该算法的性能,我们首先找到一种方法将其应用于若干NP难问题:最大割、最小划分、最大团、最大加权独立集。随后,这些算法在量子模拟器上以超过一百个节点的图规模进行了测试,并在真实量子计算机上测试了高达256个节点的图规模。据我们所知,这些构成了迄今为止在NISQ设备上运行过的最大规模现实组合优化问题,将此前的问题规模提高了近十倍。

英文摘要:

NP-hard problems are not believed to be exactly solvable through general polynomial time algorithms. Hybrid quantum-classical algorithms to address such combinatorial problems have been of great interest in the past few years. Such algorithms are heuristic in nature and aim to obtain an approximate solution. Significant improvements in computational time and/or the ability to treat large problems are some of the principal promises of quantum computing in this regard. The hardware, however, is still in its infancy and the current Noisy Intermediate Scale Quantum (NISQ) computers are not able to optimize industrially relevant problems. Moreover, the storage of qubits and introduction of entanglement require extreme physical conditions. An issue with quantum optimization algorithms such as QAOA is that they scale linearly with problem size. In this paper, we build upon a proprietary methodology which scales logarithmically with problem size - opening an avenue for treating optimization problems of unprecedented scale on gate-based quantum computers. In order to test the performance of the algorithm, we first find a way to apply it to a handful of NP-hard problems: Maximum Cut, Minimum Partition, Maximum Clique, Maximum Weighted Independent Set. Subsequently, these algorithms are tested on a quantum simulator with graph sizes of over a hundred nodes and on a real quantum computer up to graph sizes of 256. To our knowledge, these constitute the largest realistic combinatorial optimization problems ever run on a NISQ device, overcoming previous problem sizes by almost tenfold.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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