Accelerating Voting by Quantum Computation

Abstract: 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.