二元线性规划的量子约束生成框架

IF 5.6 2区 物理与天体物理 Q1 OPTICS
András Czégel, Boglárka G.-Tóth
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引用次数: 0

摘要

我们提出了一种利用量子计算机进行二进制线性规划(BLP)的新方法,该方法可以推广到一般整数线性规划(ILP)。量子优化算法,混合或纯量子,目前是通用的,独立的求解ILP。然而,考虑到它们的实际用途,我们期望它们的性能优于当前最先进的经典求解器。这种期望对量子算法是不公平的:在经典的ILP求解器中,经过几十年的进化,许多不同的算法作为一个强大的机器一起工作,以获得最佳结果。这就是我们现在想用量子“解算器”解决方案来遵循的方法。在本研究中,我们将任何合适的量子优化算法封装到量子信息经典约束生成框架中。首先,我们通过去掉所有约束来放松问题,并将其编码为量子优化子程序的伊辛哈密顿量。然后,通过从子例程的解状态中采样,我们获得了初始问题中约束违反的信息,从中我们决定需要将哪些耦合项引入哈密顿量。耦合项对应于初始二元线性规划的约束条件。然后我们再次对新的哈密顿函数进行优化,直到我们得到一个可行的解,或者其他停止条件成立。由于人们可以决定在单个步骤中向哈密顿量添加多少约束,因此我们的算法至少与它封装的(混合)量子优化算法一样有效。我们支持我们的索赔,结果是小规模,最低成本,准确覆盖问题实例。
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 constraint generation framework for binary linear programs

We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum ‘solver’ solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.

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来源期刊
EPJ Quantum Technology
EPJ Quantum Technology Physics and Astronomy-Atomic and Molecular Physics, and Optics
CiteScore
7.70
自引率
7.50%
发文量
28
审稿时长
71 days
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following: Quantum measurement, metrology and lithography Quantum complex systems, networks and cellular automata Quantum electromechanical systems Quantum optomechanical systems Quantum machines, engineering and nanorobotics Quantum control theory Quantum information, communication and computation Quantum thermodynamics Quantum metamaterials The effect of Casimir forces on micro- and nano-electromechanical systems Quantum biology Quantum sensing Hybrid quantum systems Quantum simulations.
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