Experimental Implementation of the Quantum Volunteer's Dilemma on NISQ Hardware: Noise Analysis and Digital-Twin Validation
Germán D. Díaz Agreda, Jhon Alejandro Andrade Hoyos, Carlos A. Durán Paredes, Sebastián Cajas Ordoñez, Noah Dane Hebdon, Siong Thye Goh, Dax Enshan Koh
quant-phSubmitted May 29, 2026• Announced Jun 1, 2026• 0 citations
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 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 evaluate calibration-based digital twins for IBM Quantum hardware, aiming to reproduce hardware measurement outcomes on classical simulators. We present a workflow that builds twins from downloadable calibration CSV files by mapping coherence times, gate and readout error rates, and operation durations to thermal-relaxation, depolarizing, and readout error channels, while reconstructing a directed coupling map to restore connectivity constraints during transpilation. We compare four twin variants (CSV-built, backend-derived simulator, backend-derived noise model, and fake-backend snapshots) under a common execution and validation protocol. Experiments on two IBM QPUs, ibm_brisbane and ibm_sherbrooke, use randomized five-qubit circuits of depths 10, 20, and 30 across four optimization levels. Weighted Jaccard similarity indicates that twins constructed from downloadable calibration CSV data often achieved the closest agreement with hardware, while backend-derived twins provided competitive and practical baselines. The results further show that agreement depends on both the target device and the transpilation settings, underscoring the need to validate digital twins for the specific execution setup rather than assuming transferability across devices.
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.
A well-known model in game theory, the Volunteer's Dilemma describes a group of n players who decide whether to volunteer for a collective benefit at a personal cost, or to abstain and risk forfeiting the benefit altogether. A quantum version of this dilemma, developed within the Eisert-Wilkens-Lewenstein framework, allows each player to manipulate one qubit of a shared entangled state, leading to symmetric Nash equilibria with higher expected payoffs than in the classical game. Existing analyses, however, assume maximal entanglement, which is experimentally demanding for hardware-constrained quantum systems. Within the same framework, we introduce a generalized Quantum Volunteer's Dilemma with a tunable entanglement parameter γ and study the extent to which equilibrium behavior depends on the level of entanglement. We derive explicit conditions relating γ, the number of players, and the players' strategies under which symmetric Nash equilibria exist, focusing on two canonical strategy profiles: one for 2≤n≤9, and one for even n. We find that maximal entanglement is not required to sustain symmetric equilibria. Instead, equilibrium behavior persists above a threshold value, which we compute analytically in both cases. We also demonstrate that the threshold value directly depends on system size.
This paper investigates the strategic implications of quantum mechanics on the N-Player Public Goods Game (PGG), a canonical model for the "Tragedy of the Commons." Classically, the PGG is dominated by a single, socially suboptimal Nash Equilibrium where all players 'defect' (free ride), leading to a collective loss. We investigate whether quantum strategies, specifically those that utilize multi-particle entanglement, can overcome this problem. We construct and evaluate three different strategies—a classical 'All Defect' benchmark, an 'Independent Quantum' strategy using superposition, and a 'Coordinated Quantum' strategy using an N-qubit entangled state—for N = 4 and N=5 player games and different pot multipliers (m = 1. 5, 2. 0). These techniques are run on a noise model calibrated to the IBM ibmq_manila quantum device, giving an honest estimate of performance on near-term hardware. Methodologically, we use repeated simulation for statistical robustness, reporting numbers with 95% confidence intervals. Our results exhibit a deep and statistically significant quantum benefit: the entangled approach systematically forms a cooperative Quantum Nash Equilibrium that achieves almost optimal payoffs, far surpassing the classical and independent quantum methods. Nevertheless, an extensive examination of the noise mechanisms at play shows that the scalability of this quantum solution is inherently limited in the Noisy Intermediate-Scale Quantum (NISQ) era. The interaction between error accumulation in the CNOT cascade needed for state preparation and the intrinsic decoherence of the entangled GHZ state produces an escalating failure mechanism that puts a bound on the realizable size of the game. This paper thereby offers both evidence of quantum advantage over a social dilemma and a realistic appraisal of the hardware-dictated constraints that will have to be overcome before such solutions are scalable.
A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average 2.9x (and up to 18x) improvement in program success rate over the industry standard IBM Qiskit compiler. Despite small qubit counts, NISQ systems will soon be large enough to demonstrate "quantum supremacy", i.e., an advantage over classical computing. Tools like ours provide significant improvements in program reliability and execution time, and offer high leverage in accelerating progress towards quantum supremacy.