Studying the computational complexity of determining winners under voting rules and designing fast algorithms are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum computing. We propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. We further show that our algorithm can be quadratically faster than any classical algorithm (based on sampling with replacement) under a wide range of common voting rules, including positional scoring rules, Copeland, and single transferable voting (STV). Precisely, our quantum-accelerated voting algorithm output the correct winner with runtime $\Theta\left(\frac{n}{\text{MOV}}\right)$, where $n$ is the number of votes and $\text{MOV}$ is margin of victory, the smallest number of voters to change the winner. On the other hand, any classical voting algorithm based on sampling with replacement requires runtime $\Omega\left(\frac{n^2}{\text{MOV}^2}\right)$ under a large subset of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

翻译：研究确定投票规则下获胜者的计算复杂性问题以及设计快速算法，是计算社会选择领域的经典基础课题。本文通过量子计算加速投票过程，提出一种可应用于任意匿名投票规则的量子加速投票算法。我们进一步证明，在包括位置计分规则、科佩兰规则和单一可转移投票（STV）在内的多种通用投票规则下，该算法相较于任何经典算法（基于有放回抽样）可实现平方级加速。具体而言，量子加速投票算法输出正确获胜者的运行时间为 $\Theta\left(\frac{n}{\text{MOV}}\right)$，其中 $n$ 为投票总数，$\text{MOV}$ 为获胜边际（即改变获胜结果所需的最小选民数）。而基于有放回抽样的经典投票算法在大部分投票规则下需要 $\Omega\left(\frac{n^2}{\text{MOV}^2}\right)$ 的运行时间。我们在多数制、博达计分制、科佩兰规则和STV规则下的实验结果均验证了理论结论。