Nonlocality as a Benchmarking Tool for Quantum Processors

AI summary

Overview

Research area: Quantum computing hardware benchmarking / quantum foundations (Bell-type nonlocality tests), with experimental work on superconducting and trapped-ion processors.

Technical level: Intermediate. The reader benefits from knowing what Bell inequalities, GHZ states and gate fidelities are, but the protocol itself is explained operationally.

One-sentence scope: The paper turns the violation of the Svetlichny inequality — an inequality designed to certify genuine multipartite nonlocality — into a practical benchmark and applies it, alongside Mermin's inequality, to two architecturally different quantum processors (IQM's superconducting Garnet and AQT's ion-trap Marmot) using GHZ states and two families of random circuits for three to five qubits.

What This Paper Is About

Quantum processors are hard to compare: different vendors report different metrics, and standard benchmarks say little about how well a device builds up correlations across many qubits at once. The authors ask whether a device can reproduce the correlations needed to violate the Svetlichny inequality, which rules out all hybrid local-realistic models and therefore probes correlations that are genuinely spread over all qubits rather than confined to a subset. The goal is to show that this "simulated nonlocality" test is a stringent, informative benchmark that can rank two distinct hardware architectures and even reveal differences between qubit subsets inside a single chip.

Key Contributions

1. A Svetlichny-based benchmarking protocol, developed and deployed at scale. Building on the framework of Ref. [19], the authors define a procedure that generates random quantum circuits, numerically optimizes local measurement settings for each circuit, records the distribution of Svetlichny operator expectation values, and tracks how that distribution degrades under noise. The violation fraction relative to the ideal (noiseless) case is the headline quantity, with Maximum Mean Discrepancy (MMD) added to quantify changes in the full distribution.

2. Numerical evidence that the Svetlichny test is stricter than the Mermin test. Under one-qubit depolarizing noise with two-qubit noise set to twice the single-qubit value, the Svetlichny relative violation percentage falls faster than Mermin's for N = 3, 4 and 5 qubits, and the MMD between ideal and noisy distributions grows faster for Svetlichny. Grover's algorithm success probability (single marked element in a database of 2^N elements, N = 3, 4, 5) is used as an algorithmic reference point.

3. A controlled head-to-head experiment on two architectures under identical logical circuits. The same circuits were run on Garnet (20 superconducting qubits, square lattice with tunable couplers, quantum volume 32) and Marmot (16 ion-trap qubits, 12 available at the time of the experiments, all-to-all connectivity, quantum volume 128), with 10^5 random circuits generated per family and qubit number and representative circuits selected across the nonclassical region. Three circuit families were probed: GHZ states, Clifford-only circuits (H, S, CNOT; non-universal) and Clifford + T circuits (universal).

4. Spatial and calibration-resolved testing. Simultaneous triplet tests were run across the full Marmot register, and on Garnet different qubit subsets were compared using native gates at different calibration times, probing how Svetlichny violations depend on qubit location and calibration. The abstract also reports a comparison between GHZ and linear cluster states.

Main Findings

• Svetlichny violations collapse on Garnet beyond three qubits. In the GHZ tests, the normalized violation ratio R for the Svetlichny inequality on Garnet is −0.08 at N = 4 and −0.55 at N = 5, meaning the measured value sits at or below the hybrid local realism bound. The corresponding Garnet values are 7.72 ± 0.09 (N = 4) and 12.3 ± 0.50 (N = 5) against theoretical values of 11.31 and 22.62.

• Mermin violations survive on Garnet for all tested sizes. For 2 ≤ N ≤ 5, Garnet's Mermin results stay inside the nonclassical region: 1.54 ± 0.02 (N = 3), 1.91 ± 0.06 (N = 4) and 2.18 ± 0.05 (N = 5), against theoretical 2, 2.82 and 4.

• Marmot outperforms Garnet on the same logical circuits. Marmot's GHZ Svetlichny values are 5.39 ± 0.05 (N = 3), 9.83 ± 0.26 (N = 4) and 18.68 ± 0.74 (N = 5), with R = 0.84, 0.55 and 0.40 respectively, all positive. Mean relative error ε_rel for Svetlichny on Marmot is 4.6, 13.1 and 17.4 percent, versus 22.3, 31.7 and 45.5 percent on Garnet.

• The two-qubit case is also reported for reference. CHSH (N = 2): theoretical 1.41; Garnet experimental 1.22 ± 0.03 with ε_rel 13.5 and R 0.54; Marmot experimental 1.36 ± 0.10 with ε_rel 3.9 and R 0.87.

• Universal (Clifford + T) random circuits show the same pattern. Svetlichny is violated only in the last sub-interval (State 6) for three qubits, and no Svetlichny violation is observed anywhere in the nonclassical region for four and five qubits, while Mermin violations persist for all N considered.

• The Svetlichny test is the harder test, by design and by measurement. The authors attribute the faster degradation to its dependence on higher-order correlations, so that decoherence, imperfect two-qubit gates and loss of phase coherence are amplified even when the per-term relative error resembles the Mermin case.

• For five qubits, Svetlichny tracks algorithmic performance more closely than Mermin. In the noise simulations, the Svetlichny relative violation fraction for N = 5 follows the degradation of Grover's success probability more closely than the Mermin fraction does.

• Noise models do not fully capture the hardware. Calibrated simulators (FakeAdonis for Garnet, AQT Provider for Marmot) were run alongside the devices, and deviations from the measured data are used to identify effects the reported noise models miss. For example, Marmot's Svetlichny simulation reaches 21.30 ± 0.10 at N = 5, above the measured 18.68 ± 0.74.

• The test is not a loophole-free nonlocality certification. Because all qubits sit in one cryostat or trap, space-like separation cannot be enforced; following Ref. [19], the authors describe the protocol as simulating nonlocality and note the correlations can be reinterpreted as a form of contextuality.

Methodology in Plain English

The inequality side. Mermin's inequality asks whether correlations can be explained by a fully local hidden-variable model. Svetlichny's inequality asks a stricter question: whether they can be explained by a hybrid model in which nonlocality is allowed inside a subgroup of qubits but not across all of them. To test either, each qubit is measured along one of two directions on the Bloch sphere, and the expectation value of a signed combination of measurement outcomes (the Mermin or Svetlichny operator) is compared against a classical bound — 1 for Mermin, 2^(N−1) for Svetlichny.

The protocol, step by step. Generate a large set of random circuits (10^4 in simulation, 10^5 per family and qubit number for the experimental campaign). For each circuit, numerically optimize the 2N measurement directions to maximize the operator's expectation value. Build a histogram of violation values for the ideal, noiseless case. Repeat with a calibrated noise model or on real hardware. The ratio of the noisy violation count to the ideal violation count gives a relative violation percentage between 0 and 1, and the MMD measures how much the whole distribution shifted, not just how many circuits dropped below threshold.

Practical circuit selection. Running every circuit on hardware is too expensive, so the nonclassical region was split into five equal sub-intervals, and from each one the circuit with the highest violation, lowest depth and fewest CNOTs was chosen. This was applied to the Clifford + T family. Clifford-only circuits form a discrete set tied to stabilizer states, so only the depth and CNOT-count criteria were used there. Initial theoretical histograms used depths of 55 to 75 layers, but for four and five qubits almost no circuits violated Svetlichny even ideally, so depths were reduced to 3 to 15 layers.

Execution details. All experiments ran between December 2024 and June 2025 at the Leibniz Supercomputing Centre in Garching. Shots per circuit were 2000 on Garnet and 200 on Marmot (the maximum allowed per job), and each data point is a mean over 20 experimental repetitions with one-standard-deviation error bars. Because the same logical circuits were executed on both chips, the comparison includes compilation: Garnet's fixed square lattice requires SWAP-based routing for non-adjacent qubits, whereas Marmot's all-to-all connectivity does not.

Scoring. Three quantities are used throughout: ε_rel, the mean relative error against the theoretical prediction; R, the measured violation normalized between the classical and quantum bounds; and Δ, the absolute gap between the mean violations of the two devices.

Why This Matters

Impact on research. The work argues that genuine multipartite nonlocality tests, and not just ordinary multipartite Bell tests, deserve a place in the standard benchmarking toolbox alongside randomized benchmarking, quantum volume, cross-entropy benchmarking, cycle benchmarking and mirror circuits. It also supplies the comparative evidence the earlier framework lacked: Svetlichny degrades faster under noise than Mermin, and there are explicit experimental regimes where Mermin is violated while Svetlichny is not — exactly the regime Garnet enters at four and five qubits. That gap is what makes the test informative rather than redundant.

Real-world applications.

• Calibration feedback: locating poorly performing qubit subsets and re-calibrating around them, since the test resolves differences between subsets within one chip.
• Hardware procurement and platform selection: a single protocol that ranks fundamentally different architectures (superconducting versus trapped ion) on identical logical circuits.
• Compiler and routing evaluation: because both chips ran the same logical circuits but different compiled ones, the scores reflect full-stack performance including SWAP overhead.
• Algorithm-readiness screening: correlating benchmark scores with the success probability of an actual algorithm (Grover here; phase estimation or Bernstein-Vazirani are named as interchangeable) to predict application-level performance.

Industry relevance. HPC centres such as LRZ integrating quantum devices into supercomputing infrastructure need vendor-neutral, end-to-end metrics. A benchmark that degrades measurably at the exact qubit count where a device stops reproducing genuine multipartite correlations gives a concrete threshold for what workloads a machine can and cannot support.

Future Directions

• Extend beyond five qubits. The Svetlichny violation fraction was already extremely small in ideal simulation for four and five qubits at depths of 55 to 75 layers, and the step-like behavior at N = 5 was attributed to the shrinking number of violating states. Scaling the protocol will require either deeper, better-targeted circuit selection or new inequalities.

• Separate hardware from compilation more explicitly. The Garnet/Marmot comparison deliberately bundles hardware and compilation layer, since Garnet needs SWAP routing and Marmot does not. Isolating routing overhead from gate error would sharpen the diagnosis.

• Close or formally reinterpret the loopholes. The authors state that the locality loophole cannot be avoided on a colocated QPU and interpret the measured correlations as contextuality. A dedicated contextuality-based formulation, or a version of the test on separated nodes, is the natural next step.

• Map violation strength onto calibration and layout. The abstract frames simultaneous triplet tests and GHZ-versus-linear-cluster comparisons as a way to probe dependence on qubit location and calibration; turning those spatial maps into an automated calibration loop is the practical follow-on.

• Improve statistical resolution. Marmot was limited to 200 shots per job versus 2000 for Garnet, and Appendix A analyses stability as a function of shot count. Larger samples would tighten the comparison at four and five qubits.

Target Audience

Experimental quantum-computing teams and benchmarking specialists who need vendor-neutral, correlation-level metrics; HPC and research-infrastructure staff evaluating quantum hardware for integration; quantum-foundations researchers interested in what Bell and Svetlichny inequalities actually measure when the locality loophole is open; and graduate students in quantum information looking for a worked example of taking a foundational inequality from numerical noise study to two-processor experimental comparison. Readers without familiarity with Bell inequalities and Pauli measurements will find Sections II and III demanding.

Authors’ abstract

Benchmarking quantum processors is a central task in every roadmap aimed at quantum advantage. Here, we discuss a benchmarking protocol based on the violation of the Svetlichny inequality, which is designed to simulate genuine multipartite nonlocality. We compare it with Mermin's inequality, and present the results of applying this framework to two different quantum processing units -the superconducting system Garnet (from IQM) and the ion-trap system Marmot (from AQT), testing different families of quantum circuits for three to five qubits under identical experimental conditions. We also run simultaneous triplet tests across the full register, including a comparison between GHZ and linear cluster states, to probe how Svetlichny-inequality violations depend on qubit location and calibration. Our results demonstrate that tests based on genuine multipartite nonlocality provide a powerful tool to characterize the collective performance of quantum devices and to guide their calibration and optimization.