Implementation and Analysis of Quantum Majority Rules under Noisy Conditions

TL;DR

This paper evaluates the quantum majority rule (QMR) voting protocol under realistic noisy quantum conditions, analyzing its robustness and exploring entanglement-based variants to understand multi-voter quantum correlations.

Contribution

It provides the first detailed analysis of QMR's behavior on noisy quantum hardware and introduces an entanglement-based variant for testing quantum correlations in voting.

Findings

Moderate noise does not alter QMR's qualitative behavior.

Strong noise shifts societal rankings away from classical winners.

Entanglement-based variants respond differently to noise, revealing quantum correlation effects.

Abstract

Quantum voting, inspired by quantum game theory, provides a framework in which the quantum majority rule (QMR) constitution of Bao and Yunger Halpern [Phys. Rev. A 95, 062306 (2017)] violates the quantum analogue of Arrow's impossibility theorem. We evaluate this QMR constitution analytically on classical profile data and implement its final measurement stage as a quantum circuit, running on both noiseless simulators and noisy IBM quantum hardware to map how realistic noise deforms the resulting societal ranking distribution. Moderate-high single-qubit noise does not change the qualitative behavior of QMR, whereas strong noise shifts the distribution toward other dominant winners than the classical one. We quantify this behavior using winner-agreement rates, Condorcet-winner flip rates, and Jensen-Shannon divergence between societal ranking distributions. In a second, exploratory component, we demonstrate an explicitly entanglement-based variant of the QMR constitution that serves as a testbed for multi-voter quantum correlations under noise, which we refer to as the QMR2-inspired variant. There, GHZ-type and separable superpositions over opposite rankings have the same expectation values but respond very differently to noise. Taken together, these two components connect the abstract QMR constitution to concrete implementations on noisy intermediate-scale quantum (NISQ) devices and highlight design considerations for future quantum voting protocols.