Accelerating Voting by Quantum Computation

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 voting algorithm that can be applied to any anonymous voting rule. We further show that our algorithm can be quadratically faster than any classical sampling algorithm under a wide range of common voting rules, including plurality, Borda, Copeland, and STV. Precisely, our quantum voting algorithm achieves an accuracy of at least $1 - \varepsilon$ with runtime $\Theta\left(\frac{n\cdot\log(1/\varepsilon)}{\text{MOV}}\right)$, 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 a subset of voting achieves the same accuracy with runtime $\Theta\left(\frac{n^2\cdot\log(1/\varepsilon)}{\text{MOV}^2}\right)$ [Bhattacharyya and Dey, 2021]. Our theoretical results are supported by experiments under the plurality and Borda rule.