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 advan-tages 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 decisionmaking systems.
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(π/4),R(π)) were evaluated across 31 entanglement valuesγ∈[0,π]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 within3.5%−12%relative error. These findings show that quantum advan-tages 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 decisionmaking systems.
We present an experimental implementation of the multiplayer Quantum Volunteer's Dilemma on noisy intermediate-scale quantum (NISQ) hardware, executed on the ibm_kingston backend via Qiskit Runtime. The game is evaluated for N = 2 to 9 players under four transpiler optimization levels, with 20 independent repetitions per configuration and 2048 shots per circuit, including post-processing readout error correction via mthree. Target-state fidelity decays with system size but remains above 70% (corrected) through N = 9. With readout correction, the global average payoff reproduces the quantum theoretical benchmark exactly for N <= 6 and exceeds the classical Nash equilibrium across the full tested range. Optimization level 2 is selected as the reference configuration after gate count analysis reveals that levels 2 and 3 produce identical transpiled circuits, with level 2 achieving superior fidelity stability. A Hamming distance analysis of raw measurement counts shows that single-qubit errors dominate at small N, with multi-qubit contributions growing beyond N = 6. A calibration-based digital twin captures global payoff trends but exhibits a linear fidelity decay profile that diverges from the hardware behavior at large N, exposing the limits of first-order independent per-qubit noise models. These results demonstrate that aggregate quantum advantage in multiplayer games is robust to NISQ noise conditions across the full tested range, while the practical observability of state-level advantage is constrained to N <= 8 under post-processed readout correction.
Abstract We present an experimental implementation of the multiplayer Quantum Volunteer's Dilemma on noisy intermediate-scale quantum (NISQ) hardware, executed on the ibm_kingston backend via Qiskit Runtime. The game is evaluated for N = 2 to 9 players under four transpiler optimization levels, with 20 independent repetitions per configuration and 2048 shots per circuit, including post-processing readout error correction via mthree. Target-state fidelity decays with system size but remains above 70% (corrected) through N = 9. With readout correction, the global average payoff reproduces the quantum theoretical benchmark exactly for N ≤ 6 and exceeds the classical Nash equilibrium across the full tested range. Optimization level 2 is selected as the reference configuration after gate count analysis reveals that levels 2 and 3 produce identical transpiled circuits, with level 2 achieving superior fidelity stability. A Hamming distance analysis of raw measurement counts shows that single-qubit errors dominate at small N, with multi-qubit contributions growing beyond N = 6. A calibration-based digital twin captures global payoff trends but exhibits a linear fidelity decay profile that diverges from the hardware behavior at large N, exposing the limits of first-order independent per-qubit noise models. These results demonstrate that aggregate quantum advantage in multiplayer games is robust to NISQ noise conditions across the full tested range, while the practical observability of state-level advantage is constrained to N ≤ 8 under post-processed readout correction.
We experimentally study error mitigation and finite-shot sampling on superconducting quantum hardware under a constrained execution budget. The study combines calibration-aware qubit selection, circuit-depth scaling, zero-noise extrapolation, dynamical decoupling, readout-error mitigation, and repeated-shot estimation on an IBM Quantum processor. Experiments are organized across ideal simulation, noise-model simulation, and physical-device execution to separate sampling uncertainty from device-induced error. We investigate how mitigation performance changes with circuit depth, effective noise scale, qubit connectivity, and measurement budget, and quantify accuracy using expectation-value error, mean-squared error, statistical uncertainty, and mitigation gain. A fixed hardware-execution budget is used to evaluate shot allocation strategies and repeated measurements without relying on unlimited sampling. The resulting analysis provides a hardware-aware characterization of when mitigation improves expectation-value estimation and when finite-shot fluctuations offset the benefit of additional mitigation overhead. The implementation uses contemporary Qiskit and IBM Quantum Runtime workflows and is designed to provide reproducible experimental evidence for error-mitigation studies on current quantum processors.
Real life situations where there are strategies to be chosen in order to obtain a profit can be reproduced by games, so game theory is a way to describe the evolution of possible scenarios where players can select a scheme of play. Game theory takes importance in many areas, such as people decisions making, where their choices do affect others benefit (Davis, 1970; Myerson, 1991). It is to remark that the principles of game theory were initiated by trying to understand the behavior of economic strategies, however Von Neumann presented the concept of modern game theory in 1944 (Von Neumann & Morgenstern, 1947). Quantum mechanics is a tool that creates another point of view for the traditional game theory due to multiple strategies offered for the players, whom possibilities are numerously expanded in contrast of classical ones (Eisert & Wilkens, 2000). There are also games where the player who uses quantum strategies, enhances his payoffs or even always wins against a player who only uses classical moves (Meyer, 1999). It is to remark that there are plenty of applications for quantum game theory such as quantum cryptography and computation, economics and biology (Piotrowski & Sladkowski, 2003; Hanauske et al.,2009). The Battle of the Sexes game is a largely analyzed problem, based on two players: Alice and Bob and their choice about an activity for a Saturday night with each other. It is pretty important to remark that both want the best possible payoff in the decision, so the game can be developed normally, otherwise it would not be our case. Alice, really loves Opera, but wants to be with Bob; Bob likes Football but he wants to have Alice’s company along the activity. This game has a lot of applications in real life scenarios such as the spread of some type of genes from a reproduction between two organisms (Dawkins, 2006); another interesting application is neuroeconomics (Montague & Berns, 2002), where brain studies have been done in order to incite neurons to choose either to “work” for a reward or to “shirk” (Glimcher, 2003).
Abstract Multiplayer quantum games have received growing attention due to the ability of quantum computational models to access enlarged strategic spaces, thereby enabling the emergence of nonclassical Nash equilibria and Pareto-efficient solutions. Concurrently, graph-theoretic representations have become a standard tool for encoding relational dependencies among interacting players. This work establishes a unified formalism that embeds arbitrary graph topologies into parametrized quantum-game circuits, providing a direct mapping between network structure and the strategic interaction space of quantum players. Within this framework, we analytically and computationally evaluate how graph-induced interpersonal couplings modulate payoff distributions over repeated quantum-game iterations. In addition, we integrate a reward-driven adaptation algorithm that allows players to optimize their local strategy parameters dynamically with respect to accumulated payoffs. Experimental results demonstrate that the equilibrium reward landscape is highly sensitive to the players’ graph-theoretic centrality and the weighted structure of their adversarial and cooperative relationships.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.