用量子近似优化算法击败二元喷漆车间问题的经典启发式算法
Beating classical heuristics for the binary paint shop problem with the quantum approximate optimization algorithm
AI总结：
本文提出用恒定深度的量子近似优化算法（QAOA）求解二元喷漆车间问题，证明在无穷大极限下平均性能优于经典启发式，并通过数值和离子阱量子实验验证。
摘要：
二元喷漆车间问题（BPSP）是汽车工业中的一个APX-hard优化问题。在这项工作中，我们展示了如何使用量子近似优化算法（QAOA）来寻找BPSP的解，并证明在无穷大极限$n\rightarrow\infty$下，恒定深度的QAOA平均而言能够击败经典启发式算法。对于BPSP，已知不存在任何经典算法能够在多项式运行时间内近似该问题。我们引入了一个QAOA难以求解的BPSP实例，并数值研究了其性能，同时讨论了QAOA生成近似解的能力。我们通过在AWS Braket上的 trapped-ion 量子计算机上运行小规模实例的首次实验来完善我们的研究。
英文摘要：
The binary paint shop problem (BPSP) is an APX-hard optimization problem of the automotive industry. In this work, we show how to use the Quantum Approximate Optimization Algorithm (QAOA) to find solutions of the BPSP and demonstrate that QAOA with constant depth is able to beat classical heuristics on average in the infinite size limit $n\rightarrow\infty$. For the BPSP, it is known that no classical algorithm can exist which approximates the problem in polynomial runtime. We introduce a BPSP instance which is hard to solve with QAOA, and numerically investigate its performance and discuss QAOA's ability to generate approximate solutions. We complete our studies by running first experiments of small-sized instances on a trapped-ion quantum computer through AWS Braket.
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