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Implementation and analysis of quantum majority rules under noisy conditions.
Gal Amit1, Yuval Idan1, Michael Suleymanov1
1Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan, 5290002, Israel.
Scientific Reports
|June 1, 2026
Summary
Quantum voting protocols, like the quantum majority rule (QMR), can violate Arrow's theorem. Noise in quantum hardware affects voting outcomes, but QMR shows resilience, with design considerations for future quantum voting systems.
Area of Science:
- Quantum Information Science
- Computational Social Science
- Quantum Computing
Background:
- Quantum game theory offers novel voting frameworks, such as the quantum majority rule (QMR) constitution.
- The QMR constitution has been shown to violate the quantum analogue of Arrow's impossibility theorem.
Purpose of the Study:
- To evaluate the QMR constitution's performance on classical data and its implementation on quantum hardware.
- To analyze the impact of realistic noise on the societal ranking distribution and voting outcomes.
- To explore an entanglement-based variant for multi-voter quantum correlations under noise.
Main Methods:
- Analytical evaluation of QMR on classical profile data.
- Implementation of QMR's measurement stage as a quantum circuit on simulators and noisy IBM quantum hardware.
- Quantification of noise effects using winner-agreement rates, Condorcet-winner flip rates, and Jensen-Shannon divergence.
- Development and analysis of a QMR2-inspired variant using entanglement.
Main Results:
- Moderate noise preserves QMR's qualitative behavior, while strong noise can alter dominant winners and societal rankings.
- QMR trends persist across various profile geometries, but robustness depends on proximity to cycle-dominated structures.
- Randomized electorates show profile-to-profile sensitivity to noise even in the noiseless limit.
- The QMR2-inspired variant demonstrates noise-fragile multi-voter quantum correlations.
Conclusions:
- The study connects abstract QMR to practical noisy intermediate-scale quantum (NISQ) device implementations.
- Noise significantly impacts quantum voting outcomes, necessitating careful design considerations.
- Findings inform the development of future quantum and quantum-inspired voting protocols.
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