量子博弈论中理论与实践的桥梁：在NISQ硬件上实现带误差缓解的性别之战优化方案

摘要

在真实硬件上实现量子博弈论面临噪声、退相干和量子比特连接性有限等挑战，然而此类实验验证对于理论预测的确认至关重要。我们首次在IBM Quantum的ibm sherbrooke超导处理器上，基于Eisert-Wilkens-Lewenstein（EWL）框架，完整实验实现了“性别之战”博弈。通过评估四种量子策略（I、H、R(π/4)、R(π)）在31个纠缠参数γ∈[0, π]下的表现，每个配置采用2048次采样，实现了理论预测与硬件执行之间的直接对比。为减轻噪声和变异性，我们引入了一种引导式电路映射（GCM）方法，该方法根据实时拓扑和校准数据动态选择量子比特对并优化路由。理论模型预测相较于经典均衡策略的收益提升可达108%，尽管存在硬件引入的偏差，采用GCM的实验结果仍将预期收益趋势保持在3.5%-12%的相对误差范围内。这些发现表明，在现实的NISQ（噪声中尺度量子）条件下，战略协调中的量子优势依然能够持续，为量子博弈论在多智能体、经济及分布式决策系统中的实际应用开辟了道路。

English

Implementing quantum game theory on real hardware is challenging due to noise, decoherence, and limited qubit connectivity, yet such demonstrations are essential to validate theoretical predictions. We present one of the first full experimental realizations of the Battle of the Sexes game under the Eisert-Wilkens-Lewenstein (EWL) framework on IBM Quantum's ibm sherbrooke superconducting processor. Four quantum strategies (I, H, R(pi/4), R(pi)) were evaluated across 31 entanglement values gamma in [0, pi] using 2048 shots per configuration, enabling a direct comparison between analytical predictions and hardware execution. To mitigate noise and variability, we introduce a Guided Circuit Mapping (GCM) method that dynamically selects qubit pairs and optimizes routing based on real-time topology and calibration data. The analytical model forecasts up to 108% payoff improvement over the classical equilibrium, and despite hardware-induced deviations, experimental results with GCM preserve the expected payoff trends within 3.5%-12% relative error. These findings show that quantum advantages in strategic coordination can persist under realistic NISQ conditions, providing a pathway toward practical applications of quantum game theory in multi-agent, economic, and distributed decision-making systems.

量子博弈论中理论与实践的桥梁：在NISQ硬件上实现带误差缓解的性别之战优化方案

Bridging Theory and Practice in Quantum Game Theory: Optimized Implementation of the Battle of the Sexes with Error Mitigation on NISQ Hardware

摘要

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