Implementation and analysis of quantum majority rules under noisy conditions

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. For the dephased profiles studied here, the post-processing steps act diagonally in the preference basis, so the ideal distributions underlying QMR’s violation of the quantum analogue of Arrow’s impossibility theorem can be computed classically before any optional quantum circuit sampling. Moderate readout and device noise generally preserve the qualitative behavior of QMR, whereas strong noise can shift the distribution toward different dominant winners or larger top-cycle structures, depending on the profile geometry. We quantify this behavior using winner–agreement rates, Condorcet-winner flip rates, and Jensen–Shannon divergence between societal ranking distributions. In addition to two representative hand-crafted profiles, we perform further robustness checks on randomized Dirichlet-sampled electorates and on cyclic and almost-cyclic near-threshold profiles, showing that the main QMR trends persist beyond the original examples while also revealing a sharp dependence on proximity to cycle-dominated majority structures. Unlike the two benchmark hand-crafted profiles, the randomized Dirichlet ensembles do not in general exhibit near-perfect robustness at very low noise, revealing substantial profile-to-profile sensitivity already near the noiseless limit. In a second, complementary 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 blocks and separable superpositions over opposite rankings have the same single-voter marginals, while their different correlation structure changes draw rates and variance in small mini-rounds; this effect is fragile under local noise and is washed out in the large-population limited-entanglement setting. 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 and quantum-inspired voting protocols.