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arXiv:2603.12622

Adversarial Stress Tests for Quantum Certification

Veronica Sanz, Augusto Smerzi

quant-phSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
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Abstract

We develop a practical framework for semi-device-independent (SDI) certification under operational deviations from the ideal protocol model. Apparent violations of classical benchmarks need not signal genuinely non-classical behaviour; they can arise from misalignment between (i) the scoring rule, (ii) the finite-sample statistical bound applied to that score, and (iii) the operational model realised in the experiment, including bias, memory, drift, and selection effects. We formalise a protocol-agnostic alignment principle based on a martingale-safe lower confidence bound and an operationally consistent effective classical ceiling. This yields a quantitative diagnostic, the \emph{robustness gap} $Δ_{\mathrm{rob}} = S_{\mathrm{low}} - S_{C,\mathrm{eff}}$, which separates statistical fluctuations from structural modelling errors. Statistical deviations vanish asymptotically, whereas model misalignment can produce persistent false certification unless the benchmark is corrected. Using the $2\!\to\!1$ random access code as a minimal SDI testbed, we show that postselection can inflate conditional scores, whereas unconditional scoring restores the correct operational meaning of the witness. We further show that adaptive learning-based classical agents do not enlarge the admissible classical set; rather, they recover the effective classical ceiling implied by the operational model. The resulting framework provides a systematic diagnostic for certification in realistic quantum communication and measurement settings with embedded classical control, adaptive processing, and nonideal data acquisition.

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We develop a practical framework for semi-device-independent (SDI) certification under operational deviations from the ideal protocol model. Apparent violations of classical benchmarks need not signal genuinely non-classical behaviour; they can arise from misalignment between (i) the scoring rule, (ii) the finite-sample statistical bound applied to that score, and (iii) the operational model realised in the experiment, including bias, memory, drift, and selection effects.
We formalise a protocol-agnostic alignment principle based on a martingale-safe lower confidence bound and an operationally consistent effective classical ceiling. This yields a quantitative diagnostic, the \emph{robustness gap} Δrob=Slow−SC,effΔ_{\mathrm{rob}} = S_{\mathrm{low}} - S_{C,\mathrm{eff}}Δrob​=Slow​−SC,eff​, which separates statistical fluctuations from structural modelling errors. Statistical deviations vanish asymptotically, whereas model misalignment can produce persistent false certification unless the benchmark is corrected.
Using the 2 ⁣→ ⁣12\!\to\!12→1 random access code as a minimal SDI testbed, we show that postselection can inflate conditional scores, whereas unconditional scoring restores the correct operational meaning of the witness. We further show that adaptive learning-based classical agents do not enlarge the admissible classical set; rather, they recover the effective classical ceiling implied by the operational model.
The resulting framework provides a systematic diagnostic for certification in realistic quantum communication and measurement settings with embedded classical control, adaptive processing, and nonideal data acquisition.
The rapid advancement of quantum hardware calls for the development of reliable methods to certify its correct functioning. However, existing certification tests often fall short: they either rely on flawless state preparation and measurement or lack soundness guarantees, meaning that they do not rule out incorrect implementations of the target operations by a quantum device. We introduce an approach, which we call quantum system quizzing, for the certification of quantum gates in a practical server-user scenario, where a classical user tests the results of quantum computation performed by a quantum server by checking its responses to a set of predesigned small-sized computational problems. Importantly, this approach does not require trusted state preparation and measurement and is thus inherently free from the associated systematic errors. For a wide range of relevant gate sets, including a universal one, we prove our certification protocol to be sound; i.e., it is guaranteed to reject any incorrect gate implementation, under the assumptions of a known Hilbert space dimension and context independence of error. A major technical challenge that we are first to resolve is recovering the tensor product structure of a multi-qubit system in the memory-bounded single-device setup. Finally, we prove the robustness of our protocol and validate its sample and computational efficiency through extensive numerical experiments. Our protocol is platform-agnostic and introduces a new paradigm for benchmarking and comparing diverse quantum architectures.
Standard quantum verification and certification protocols often assume that experimental sources emit independent and identically distributed (i.i.d.) states. In realistic scenarios, however, temporal drift, memory effects, feedback, and correlated noise can violate this assumption, causing standard analyses to underestimate uncertainty and overestimate device performance. Here, we introduce a general framework for quantum verification and certification in which the state produced in each round may depend arbitrarily on the preceding experimental history. Our method provides rigorous confidence intervals for observable expectation values averaged over the experimental trajectory. The framework covers both full verification, in which every state is measured, and spot-checking certification, in which a randomly selected subset is tested to certify the average observable value of the complementary, remaining systems. We apply the framework to importance-sampled Pauli measurements for direct fidelity estimation, energy estimation, and entanglement witnessing, and to classical shadows, allowing multiple observables to be certified simultaneously from the same test data. We illustrate the framework numerically and demonstrate it experimentally through Bell-state certification on a quantum processor.
In the development of quantum technologies, a reliable means for characterizing quantum devices, be it a measurement device, a state-preparation device, or a transformation device, is crucial. However, the conventional approach based on, for example, quantum state tomography or process tomography relies on assumptions that are often not necessarily justifiable in a realistic experimental setting. Although the device-independent (DI) approach to this problem bypasses the shortcomings above by making only minimal, justifiable assumptions, most of the theoretical proposals to date only work in the idealized setting where independent and identically distributed (i.i.d.) trials are assumed. Here, we provide a versatile solution for rigorous device-independent certification that does not rely on the i.i.d. assumption. Specifically, we describe how the prediction-based ratio (PBR) protocol and martingale-based protocol developed for hypothesis testing can be applied in the present context to achieve a device-independent certification of desirable properties with confidence interval (CI). To illustrate the versatility of these methods, we demonstrate how we can use them to certify—with finite data—the underlying negativity, Hilbert space dimension, entanglement depth, and fidelity to some target pure state. In particular, we provide examples showing how the amount of certifiable negativity and fidelity scales with the number of trials and how many experimental trials one needs to certify a qutrit state space or the presence of genuine tripartite entanglement. Overall, we have found that the PBR protocol and the martingale-based protocol often offer similar performance, even though the latter does have to presuppose any witness (Bell-like inequality). In contrast, our findings also show that the performance of the martingale-based protocol may be severely affected by one’s choice of Bell-like inequality. Intriguingly, a Bell function useful for self-testing does not necessarily give the optimal confidence-gain rate for certifying the fidelity to the corresponding target state.
Claims of quantum advantage should remain robust even when classical strategies have access to side information correlated with the benchmark under evaluation, just as Bell certification must account for measurement dependence. We formalize such correlations as benchmark dependence, a task-level generalization of measurement dependence. For every bounded-reward task, we show that the optimal benchmark-dependent classical score obeys Sη≤min⁡{1,Scl+η}S_η\leq\min\{1,S_{\mathrm{cl}}+η\}Sη​≤min{1,Scl​+η}, and construct a family of tasks that saturates this bound, showing that the linear dependence on ηηη is tight without further assumptions. For repeated product tasks with roundwise dependence, we obtain the stronger multiplicative bound Sη(n)≤(ωc+η)nS_η^{(n)}\leq(ω_{\mathrm c}+η)^nSη(n)​≤(ωc​+η)n, and extend the framework to finite-sample data, mutual-information constraints, multipartite tasks, and correlations distributed along a causal path. Applying these results to aggregated IBM hardware data, we obtain positive raw-count cycle-product certificates of 0.0812 for CHSH and 0.2178 for Mermin--GHZ, while the nine-context magic-square construction remains uncertified; readout-mitigated values are reported separately as sensitivity estimates. We also analyze a non-Bell quantum-kernel benchmark, where a label-construction variable has measured conditional dependence η^λ(Y)=0.5\widehatη_λ^{(Y)}=0.5η​λ(Y)​=0.5, above the threshold ηreq=0.375η_{\mathrm{req}}=0.375ηreq​=0.375, required to close the reported score gap, and yields perfect classical classification. The framework therefore converts a quantum--classical score separation into a quantitative lower bound on the benchmark-correlated classical information required to explain the score separation.
Recently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged. In this Rapid Communication we use the concept of quantum random access codes to construct a protocol able to certify the presence of the generalized measurements in a semi-device-independent way without employing quantum entanglement. We use semidefinite programming methods to show robustness of the protocol and characterize its statistical properties. We conclude that it allows for experimental realizations using technology currently available in laboratories.
An absolutely entangled set (AES) is a collection of states for which at least one member remains entangled under any choice of global unitary transformation. We develop a semi-device-independent framework for certifying this property from dimensionally bounded prepare-and-measure correlations. A witness value above the maximum attainable with separable preparations of a given dimension rules out every non-AES realization. To upperbound this limit, we construct a semidefinite-programming (SDP) hierarchy tailored to separable preparations. For a two-qubit random-access-code witness, the SDP upper bound and the heuristic lower bound coincide to the reported precision, yielding a concrete AES certification. We also formulate a general construction of witnesses for extended preparation sets containing target pure-state AESs. Examples based on equiangular tight frames, a minimal AES, and mutually unbiased bases further illustrate the scope of the method. In summary, our results establish a systematic and experimentally feasible approach to the certification of AESs in semi-device-independent quantum information protocols.