Quantum-Classical Separation in Bounded-Resource Tasks Arising from Measurement Contextuality

Abstract: The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

• The paper establishes that measurement contextuality enables quantum-classical separation through protocols such as the Mermin-Peres game and GHZ parity games.
• It employs a large-scale superconducting qubit processor to achieve near-perfect quantum success rates that significantly exceed classical performance limits.
• The study quantitatively analyzes error channels and demonstrates a resource advantage in hidden linear function problems, offering a new benchmark for quantum hardware.

Quantum-Classical Separation Enabled by Measurement Contextuality

Introduction

This paper rigorously investigates quantum-classical separation in bounded-resource computational and game-theoretic tasks, specifically those leveraging quantum measurement contextuality. By employing a large-scale superconducting qubit processor, the authors execute contextuality-based protocols that are known to exceed classical limits. The work provides both experimental quantification of contextuality in system sizes from few-body up to hundreds of qubits and demonstrates scenarios—via pseudo-telepathy games, Kochen-Specker-Bell inequality violation, and hidden linear function problems—where quantum resources afford superior performance relative to any classical strategy.

Quantum Contextuality: Foundation and Operationalization

The experimental agenda is grounded in the principle that quantum measurement outcomes can depend on the context of compatible co-measured observables, a property absent in any non-contextual hidden variable (NCHV) model. The paper operationalizes this property via two canonical protocols:

1. Mermin-Peres Magic Square Game: This two-player cooperative pseudo-telepathy game can be deterministically won only by quantum strategies using shared Bell pairs and measurement plans conditioned on assigned row/column contexts. The classical bound for the average winning probability is $8/9$, whereas the quantum implementation achieves $P_w = 0.9830 \pm 0.0001$ (Variation I) and demonstrates, in error-free scenarios, perfect success. The experiment further supports that quantum advantage is rooted in matrix mechanics and the non-commutativity of Pauli operators.
2. Kochen-Specker-Bell Inequality Violation: The authors quantify contextuality via ensemble averages of products of compatible observables, showing an experimental $X_{KSB} = 5.618 \pm 0.005$, versus the classical bound of 4 and the theoretical quantum limit of 6. This result significantly surpasses prior state-independent contextuality demonstrations and represents a large state-independent separation in the contextual resource.

Many-Body Contextuality: GHZ Games

The study extends contextuality benchmarks to many-body regimes through implementation of the $N$-qubit GHZ parity game. Here, up to $N=71$ players (qubits) achieve winning probabilities exceeding all classical strategies, whose best success rate converges to $1/2$ for large $N$. Quantum strategies based on sharing the $|GHZ\rangle$ state and conditional measurements in the $X$ or $Y$ basis guarantee $P_w = 1$ theoretically; experimentally measured probabilities remain above the classical ceiling even as the quantum-state fidelities and noise accumulate at scale.

The paper analytically dissects error channels (T$_1$ decay, single- and two-qubit gate errors, and readout errors) and tracks their respective contributions to GHZ state fidelity and game success rates. For all $N < 45$, the total GHZ fidelity exceeds the genuine entanglement threshold ($F > 0.5$), evidencing multipartite entanglement necessary for quantum advantage in these games.

Quantum Advantage in Hidden Linear Function Problems

Leveraging a strong equivalence between non-local games and shallow quantum circuits, the authors experimentally deploy the Bravyi et al. hidden linear function (HLF) problem on 2D qubit grids. The quantum protocol is implemented with four layers of two-qubit (CZ) gates, achieving exact probabilistic solution of the problem for matrix sizes up to $n=105$. The quantum effective depth, quantifying time-to-solution, scales favorably compared to classical lower bounds based on two-input gate layers (conjectured at $\log_2(s)$ for $s$ input bits).

Theoretical classical depth lower bounds (from Bravyi et al.) become relevant only for $n \gtrsim 10^6$; thus, near-term quantum devices can outperform classical circuits in circuit depth even in sizes accessible to current hardware. The experiment demonstrates that, even with hardware noise, contextuality-based quantum algorithms afford resource savings over classical strategies in bounded-connectivity scenarios.

Implications and Future Outlook

The results posit measurement contextuality not merely as a philosophical aspect but as a practical, quantifiable computational resource in quantum information science. Practically, contextuality-based benchmarks offer sensitive and interpretable metrics for quantum hardware characterization, outperforming purely random circuit sampling or unitary channel benchmarking. The protocols' sensitivity to coherent errors and hardware imperfections allows for more comprehensive evaluation of quantum device "quantumness" and algorithmic resilience.

Theoretically, these experiments further validate the expectation that contextuality underpins quantum advantage in both nonlocal games and circuit-based computation, supporting proposals that contextuality is a necessary and sufficient resource for universal quantum computation. The protocols designed, including scalable GHZ games and HLF circuits, lay groundwork for developing quantum algorithms and certifications rooted in contextual phenomena—extending to condensed matter ground states, quantum phase transitions, and benchmarking standards for next-generation quantum processors.

Regarding future developments, the framework encourages expansion toward deeper many-body contextuality tests (beyond shallow circuit architectures), more nuanced resource-theoretic separation theorems, and refinement of contextuality as an operational figure of merit for algorithmic and hardware scaling.

Conclusion

This work demonstrates experimental quantum-classical separation in bounded-resource tasks derived from measurement contextuality. Through large-scale implementation of the Mermin-Peres game, Kochen-Specker-Bell inequality violations, scalable GHZ parity games, and hidden linear function problems on superconducting qubit processors, the authors establish that contextuality is a tangible computational resource enabling tasks beyond classical reach. These results not only provide metrological standards for quantum hardware benchmarking but also reinforce contextuality's central role in realizing quantum advantage for both few- and many-body settings.