quantum hardware testers

Abstract: Noisy Intermediate-Scale Quantum (NISQ) hardware has transformed quantum computing into a practical experimental platform while introducing fundamental challenges associated with hardware noise, decoherence, and probabilistic execution. Although quantum software testing (QST) has rapidly emerged as an active research area, it remains unclear to what extent existing testing methodologies explicitly engage with noisy and hardware-constrained execution environments. This paper presents a systematic empirical landscape analysis of noise-awareness in QST research through a deterministic, taxonomy-guided analytical framework applied to 61 papers published between 2018 and 2025 across eight testing paradigms, contrasting how contributions are framed with how they are evaluated. Among the analyzed papers, 47 (77.0%) are noise-oblivious and only 14 (23.0%) explicitly engage with noise-related execution concerns, while only 11 (18.0%) report evaluation on physical hardware or a noisy simulator. Test generation, the largest paradigm, exhibits a noise-awareness rate of only 14.3%, and debugging and repair 18.2%; coverage-based, metamorphic, and differential testing contain no noise-aware contributions. Noise-aware methodologies emerged late and remain outnumbered in all analyzed years. Framing and evaluation are strongly associated (odds ratio 40.5, p < 0.001) yet diverge for individual papers: 5 of the 14 noise-aware papers evaluate only on ideal simulators. Inferential statistical tests are reported in only 16.4% of papers. The classification framework was validated against a blinded, human-coded reference sample, achieving almost perfect inter-rater agreement on testing-technique classification and substantial agreement on noise-awareness. The framework provides a reusable empirical basis for longitudinal analysis of hardware-conscious testing practice.

Abstract: Reliable quantum computation requires methods for verifying quantum circuits. Level-synchronized tree automata (LSTAs) were recently introduced to represent sets of quantum states for this purpose. We study LSTAs along two axes relevant to verification: the complexity of their decision problems and the size of their representations under circuit operations. We prove that acyclic LSTAs have NP-complete nonemptiness and $Π_2^P$-complete language inclusion, and that general language inclusion is EXPSPACE-complete. We further prove inherent quadratic representation growth under individual quantum gates in a fixed qubit order, and give an adjacent-qubit reordering construction that preserves level synchronization. These results clarify the scope of applicability of the automata-theoretic toolbox for quantum circuit verification.

Abstract: Quantum networking represents the future of secure communication, enabling fundamentally new capabilities through quantum information exchange. However, these networks require secure, high-fidelity quantum communication channels, and they require every participating node to be a genuine quantum device. Currently, there is no reliable method to verify whether clients entering a quantum network truly possess quantum computational capability and are connecting over robust channels. In this work, we introduce a client-validation protocol that functions as a proof-of-quantum-capability handshake. Our protocol secures a quantum network against classical spoofers, noisy quantum computers, and genuine quantum devices connecting with the network over noisy or insecure channels. We validate the efficacy of this protocol through numerical simulations under erasure, dephasing, and depolarizing noise models.

Abstract: Quantum compilers synthesize high-level operations, such as the quantum Fourier transform and multi-controlled X gates, into gate-level circuits. Across compilation stages, a circuit may be serialized, exchanged as OpenQASM, converted between compilers, or lowered to gates. These representation changes can preserve computation while removing the high-level operation itself, leaving the receiving compiler unable to apply a requested synthesis method. We call this loss synthesis availability. We study synthesis availability in Qiskit, TKET, and Cirq through controlled experiments, repository analysis, circuits captured from project tests, and a Munich Quantum Toolkit pipeline. Synthesis availability survives serialization when deserialization restores the high-level operation and survives compiler conversion only when the receiving compiler supports that operation. It does not survive the evaluated OpenQASM routes. After a direct OpenQASM 3 round trip, requested synthesis has no effect in all 360 delivered conditions even though compilation succeeds. In the MQT pipeline, OpenQASM 2 interchange increases the two-qubit gate count by 37.2 percent for an eight-qubit Grover circuit. We also introduce Verified, which records high-level operations before a representation change and reconstructs them only when a check confirms that the record still matches the delivered circuit. Verified restores requested synthesis in all 830 recovery runs, with median verification times from 2.0 to 638 ms per operation family. The check rejects every stale record but also some valid records. These results show that preserving functional equivalence alone is insufficient when later synthesis choices depend on retained high-level structure.

Abstract: We study quantum state tomography when the unknown state lies in a trace-distance ball of radius $R$ around a known reference state $ρ$. For arbitrary collective measurements, we determine the minimax expected risk and confidence radius up to universal constants, uniformly over the dimension, center spectrum, radius, and sample size. Write $Γ=d(\mathrm{Tr}\sqrtρ)^2+d^2R$. For $d\ge2$, $0<R\le1$, and $n\ge1$ copies, the expected risk is $Θ(\min\{R,\sqrt{Γ/n}\})$. At failure probability $0<δ\le1/3$, the minimax confidence radius is \[ Θ\!\left(\min\left\{R,\sqrt{\frac{Γ+\log(1/δ)}{n}}\right\}\right). \] For $\varepsilon\le c_0R$ with a universal $c_0>0$, the copy complexity is $Θ((Γ+\log(1/δ))/\varepsilon^2)$. For the lower bound we use a weighted trace-norm witness to retain all spectral scales in a square-root perturbation family. For the upper bound, we give a direct spectral and concentration analysis of a modified existing purification-based procedure.

Abstract: We give a deterministic classical algorithm that estimates $|\langle x|U|0^n\rangle|^2$ to additive error $\varepsilon$ in $\mathrm{poly}(n, 1/\varepsilon)$ time, where $U$ is a constant-depth quantum circuit comprised of gates with bounded fan-in and arbitrary connectivity, and $x$ is an arbitrary $n$-bit output string. This improves over prior state-of-the-art algorithms that takes $n^{O(log(n))}$ time for the same task, $n^{O(log(log(n))}$ when $U$ is geometrically local, and $n^{O(1)}$ for 2D geometrically-local circuits.

Abstract: We establish functional aggregate queries (FAQs) as a unifying language for exact classical simulation of quantum circuits. A circuit becomes a sum-product query: factors encode gates, internal wire variables are aggregated, and free boundary variables index transition amplitudes. The central insight is that distinct sources of simulation tractability can be exploited within the same InsideOut evaluation scheme. The query specifies what is computed; the evaluation plan, semiring, and representation of intermediate factors determine the cost. This view unifies structural and algebraic simulation guarantees. With explicit factor representations, FAQ evaluation recovers the treewidth bound for tensor-network contraction and yields finer sparsity-sensitive bounds via fractional covers. Over a formal phase semiring, compressed intermediate factors recover rank-width-based simulation for compatible quadratic phase representations. For Clifford circuits, affine-quadratic factors are closed under multiplication and marginalization and remain polynomial in size, yielding polynomial-time exact amplitude computation without any bounded-width assumption. Beyond these recoveries, the framework yields a new tractability criterion: tensor layout symmetry width. This parameter combines local cut-rank with separator symmetry through exact tree-tensor representations. We give a constructive evaluation bound and exhibit a circuit family with bounded tensor layout symmetry width but unbounded phase-graph rank-width and circuit line-graph treewidth. These results establish representation-aware FAQ evaluation as a common algorithmic foundation for classical simulation and a systematic route to new tractable regimes.

Abstract: We develop a mixing time method for estimating the sample complexity of quantum state discrimination. We start with considering the minimum-error discrimination of geometrically uniform pure state ensembles, and prove that its sample complexity has a tight estimate given by a quantum homogeneous mixing time [George et al., 2026] and a quantum version of the generalized Dobrushin coefficient [Wolfer, 2020]. This quantum mixing time further reduces to a classical one when the generating group $G$ forms a Gelfand pair with the stabilizer subgroup $H$ of the generator state. In this case the generalized Dobrushin coefficient can be fully expressed by representation-theoretic quantities of the commutative Hecke algebra $\operatorname{End}_G(\mathbb C[G/H])$. In particular, this method reduces the sample complexity estimation of learning quantum coupon collector states [Arunachalam et al., 2020] and learning phase states to classical mixing time problems. We apply this framework to answer the open problems of learning degree-$d$ phase states over $\mathbb F_q$ in [Alrabiah et al., 2026] and generalized Boolean phase states over $\mathbb Z_q$ [Arunachalam et al., 2023]. The framework also applies to hypergraph state ensembles, giving estimates expressed fully in terms of hypergraph data and recovering estimates for graph state ensembles in [Montanaro and Shao, 2022]. Finally, we extend the discussion to arbitrary mixed state ensembles with uniform priors, prove a sandwiched bound for minimum-error discrimination sample complexity by a quantum weakly mixing time, and provide a tight estimate for the minimax discrimination sample complexity from [D'Ariano et al., 2005] by a Dobrushin-type coefficient. We also discuss the method of strengthened data processing inequality [Gao and Rouz{é}, 2022] and give an upper bound in terms of a strengthened data processing inequality constant.

Abstract: Quantum channel discrimination is a primitive task for identifying, verifying, and benchmarking quantum dynamics. Previous studies have primarily considered either the best-case tester-input setting or the worst-case jammer-input setting. Here, we introduce a game-theoretic framework in which both the tester and jammer control separate inputs. Combining three input structures, characterized by whether the tester and jammer use entangled inputs or IID inputs across channel uses, with four information patterns, determined by the visibility of the jammer's strategy and its knowledge of the true hypothesis, yields twelve game models. We provide exact finite blocklength hypothesis testing characterizations of all twelve models in terms of nine minimax hypothesis testing divergences and derive their asymptotic Stein exponents. Notably, for entangled jammers, neither the visibility of the jammer's strategy nor its knowledge of the true hypothesis affects the asymptotic Stein exponent, whereas the information pattern remains consequential for IID jammers. As an example, we study the discrimination of a general channel from a replacer channel and show that all asymptotic Stein exponents coincide with the same additive, single letter quantity. We further develop a general argument that upgrades achievability results to strong converse results, thereby establishing strong converse properties for several game models, resolving an open problem in composite hypothesis testing posed by Berta et al. [Commun. Math. Phys. 385, 55 (2021)], and strengthening several recent results of Lami [arXiv:2510.06340]. The framework and techniques developed here may support future studies of quantum information tasks involving competing roles.