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arXiv:2301.02995

Accelerating Voting by Quantum Computation

Ao Liu, Han, Qishen, Lirong Xia, Nengkun Yu

Published Jan 8, 2023• 1 citation
arXivHTMLPDF

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 $Θ\left(\frac{n}{\text{MOV}}\right)$ 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 $Ω\left(\frac{n^2}{\text{MOV}^2}\right)$ time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

DOI
10.48550/arxiv.2301.02995

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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 Θ(nMOV)Θ\left(\frac{n}{\text{MOV}}\right)Θ(MOVn​) time, where nnn is the number of votes and MOV\text{MOV}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 Ω(n2MOV2)Ω\left(\frac{n^2}{\text{MOV}^2}\right)Ω(MOV2n2​) time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.
Ensuring security and integrity of elections constitutes an important challenge with wide-ranging societal implications. Classically, security guarantees can be ensured based on computational complexity, which may be challenged by quantum computers. We show that the use of quantum networks can enable information-theoretic security for the desirable aspects of a distributed voting scheme in a resource-efficient manner. In our approach, ballot information is encoded in quantum states that enable an exponential reduction in communication complexity compared to classical communication. In addition, we provide an efficient and secure anonymous queuing protocol based on a distributed secure sum. As a result, our scheme only requires modest quantum memories with size scaling logarithmically with the number of voters. This intrinsic efficiency together with certain noise-robustness of our protocol paves the way for its physical implementation in realistic quantum networks.
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We introduce a quantum voting protocol that uses superposition and entanglement to enable anonymous voting with trusted voting machines, in a centralized setting with a single machine and in a distributed setting where several machines are linked to a voting center through quantum channels. A voter selects a candidate through a restricted ballot interface; the machine encodes the vote as a phase-flip operation, controlled by the voter's identity register, on an entangled candidate state. Tallying is performed by interference with a reference branch followed by a measurement of the candidate register, which reproduces the vote distribution without iterative classical counting. Because every tallying run consumes the quantum state, the machines store the cast choices classically and replay the voting stage for each run. The protocol uses only basic quantum gates (Hadamard and controlled-Z). We provide analytical examples (4 voters with 2 candidates and 8 voters with 3 candidates) and numerical experiments that simulate ideal conditions, depolarizing, memory, readout, and gate noise, faulty or mistaken ballots, larger instances with confidence intervals, and sampling convergence. The simulations reproduce the theoretical tally probabilities in the ideal case and show how the tally is distorted by noise and by faulty ballots; no error correction or mitigation is applied. Voter anonymity is formalized as the indistinguishability of tallying transcripts under vote permutations, and an identity-dephasing step renders the identity register exactly maximally mixed under the stated trust assumptions. The numbers of protocol runs needed for exact tallying and for winner identification are analyzed explicitly.
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Quantum information protocols offer significant advantages in properties such as security, anonymity, and privacy for communication and computing tasks. An application where guaranteeing the highest possible security and privacy is critical for democratic societies is electronic voting. As computational power continues to evolve, classical voting schemes may become increasingly vulnerable to information leakage. In this work, we present the experimental demonstration of an information-theoretically secure and efficient electronic voting protocol that, crucially, does not rely on election authorities, leveraging the unique properties of quantum states. Our experiment is based on a high-performance source of Greenberger-Horne-Zeilinger (GHZ) states and realizes a proof-of-principle implementation of the protocol in two scenarios: a configuration with four voters and two candidates employing privacy enhancement techniques and an election scenario supporting up to eight voters and sixteen candidates. The latter is particularly well-suited for secure board-level elections within organizations or small-scale governmental contexts.
Anonymous voting is a voting method of hiding the link between a vote and a voter, the context of which ranges from governmental elections to decision making in small groups like councils and companies. In this paper, we propose a quantum anonymous voting protocol assisted by two kinds of entangled quantum states. Particularly, we provide a mechanism of opening and permuting the ordered votes of all the voters in an anonymous manner; any party who is interested in the voting results can acquire a permutation copy and then obtains the voting result through a simple calculation. Unlike all previous quantum works on anonymous voting, our quantum anonymous protocol possesses the properties of privacy, self-tallying, nonreusability, verifiability, and fairness at the same time. In addition, we demonstrate that the entanglement of the quantum states used in our protocol makes an attack from an outside eavesdropper and inside dishonest voters impossible. We also generalize our protocol to execute the task of anonymous multiparty computation, such as anonymous broadcast and anonymous ranking.