Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum computation: we propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. We 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 outputs the correct winner with high probability in $\Theta\left(\frac{n}{\text{MOV}}\right)$ time, where $n$ is the number of votes and $\text{MOV}$ is {\em margin of victory}, the smallest number of voters to change the winner. In contrast, any classical voting algorithm based on sampling with replacement requires $\Omega\left(\frac{n^2}{\text{MOV}^2}\right)$ time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

翻译：研究计算复杂性并设计快速算法以确定投票规则下的胜者是计算社会选择中的经典基础问题。本文通过利用量子计算加速投票：我们提出了一种可应用于任何匿名投票规则的量子加速投票算法。结果表明，在包括位置计分规则、Copeland规则及单一可转移投票（STV）在内的多种常见投票规则中，该算法的速度可达任何经典算法（基于有放回抽样）的平方级提升。具体而言，我们的量子加速投票算法能以高概率在 $\Theta\left(\frac{n}{\text{MOV}}\right)$ 时间内输出正确胜者，其中 $n$ 为票数，$\text{MOV}$ 为胜差（即改变胜者所需的最少选民数）。相比之下，基于有放回抽样的经典投票算法在大量投票规则下需要 $\Omega\left(\frac{n^2}{\text{MOV}^2}\right)$ 时间。我们在 plurality、Borda、Copeland 与 STV 规则下的实验验证了理论结果。