Jul 2026· Academia Quantum· 0 citations· 16 references
TL;DR
In these small, idealised, classically simulated matched-family tasks, the support-basis DQFIM provides a useful data-dependent pre-training diagnostic of effective capacity on the retained data support and contributes predictive information beyond raw parameter count and structural metadata.
Abstract
Introduction: Variational quantum algorithms can show unstable trainability and uneven generalisation that are not fully explained by circuit depth or raw parameter count alone. We study the data quantum Fisher information matrix (DQFIM) as a data-dependent effective-capacity diagnostic for controlled supervised unitary-learning tasks.
Materials and methods: We used exact-state, classically simulated, 4-qubit, supervised unitary-learning benchmarks with two ansatz families: a hardware-efficient ansatz (HEA) for the baseline trainability study and a symmetry-preserving ansatz for symmetry-controlled comparisons. The analysis covered four linked experiments: E0 trainability phase boundaries, E1 symmetry-controlled data-regime comparisons, E2 trainability versus generalisation, and E3 pre-training prediction of optimisation success. For the main analyses we used the support-basis DQFIM, 30 random seeds per main configuration, grouped cross-validation in the predictive benchmark, and additional diagnostics for threshold sensitivity, phase indeterminacy, Hamming-sector generalisation, and test set size sensitivity.
Results: In E0, the empirical trainability boundary increased from
M
c
=
32
at
L
=
1
to
M
c
=
192
at
L
=
8
, and the support-basis DQFIM-predicted boundary matched the empirical boundary on the resolved scanned grid under the main analysis setting. In E1, the sector-preserving and sector-broken conditions showed no resolved empirical boundary shift on the scanned grid, with only mild low-L asymmetry in the DQFIM-predicted boundary. In E2, trainability and generalisation separated clearly: some regimes generalised well, while others reached near-zero training loss but retained high test loss. The phase diagnostic supported relative phase indeterminacy as a mechanism for failure on in-sector superpositions after basis-state training. In E3, parameter count alone was a weak predictor of optimisation success, with receiver operating characteristic area under the curve (ROC AUC)
=
0.648
; the structural baseline was stronger, with ROC AUC
=
0.958
; and the DQFIM-enhanced model performed best, with ROC AUC
=
0.989
.
Conclusions: In these small, idealised, classically simulated matched-family tasks, the support-basis DQFIM provides a useful data-dependent pre-training diagnostic of effective capacity on the retained data support. It tracks resolved trainability boundaries and contributes predictive information beyond raw parameter count and structural metadata. The conclusions remain scoped to controlled small-system simulations; larger-qubit, noisy, hardware-executed, and less-matched settings require further validation before claiming practical scalability.
Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.
Jiayang Niu, Akib Karim, Yan Wang et al.· 1 citation
We present a variational algorithm for learning an unknown quantum unitary from time-series observable measurements, with no structural assumption about the target. The core separation: a hardware-efficient parametrised circuit learns the evolution operator U via observable matching; Hamiltonian identification follows as classical post-processing via matrix logarithm, when the target happens to be exp(-iH*tau). Three experiments establish the method's generality. First, a noiseless proof of correctness with exact gradients (L-BFGS-B) achieves MSE 1.61e-14 and recovers all Hamiltonian coefficients to six decimal places. Second, a gate-learning experiment fits CNOT, iSWAP, and a Haar-random SU(4) element -- none generated by any fixed Hamiltonian -- all to process fidelity 1.000000, confirming the method does not rely on Trotterisation structure. Third, quantum deployment via SPSA-Adam under Qiskit Aer depolarising noise (p1=0.001, p2=0.01, Nshots=1024) recovers all three Ising Hamiltonian terms with errors below 8%. The optimiser, SPSA-Adam, combines SPSA's hardware-efficient two-point gradient estimation with Adam's adaptive moment updates. A four-stage moment-warm curriculum progressively extends the training horizon, converting a global non-convex problem into a sequence of well-posed local ones.
Sample-based quantum diagonalization (SQD), equivalently quantum-selected configuration interaction (QSCI), has in two years become a pragmatic centre of gravity of pre-fault-tolerant quantum chemistry: a quantum processor samples electronic configurations, and the many-electron Hamiltonian is diagonalized classically in the resulting determinant subspace. Its accuracy is set entirely by which configurations enter that subspace, a selection problem for machine learning made acute by a coupon-collector bottleneck. We critically review the ecosystem of generative and learned selectors, organizing it by the object each method generates and the importance signal it exploits, and expose one conspicuous gap: a reward-proportional generative-flow-network proposer built for tail discovery. We then confront the field's central question -- whether the quantum sampler beats classical selected configuration interaction -- and report a carefully scoped negative: across published same-active-space comparisons, strong classical selected CI matches or beats the quantum-sampled subspace, and the flagship single-layer circuits now admit polynomial-time classical energy estimation. We distil a benchmarking standard and turn the negative into a regime map, then test it with FCI-exact experiments that confirm one prediction and refute another: the cheap prior's rank correlation with the exact weights declines with multireference character (a usable coordinate), but a controlled single-molecule noise sweep shows the one generative advantage we find, robustness to valid-shot starvation, to be generic rather than the multireference-specific effect a confounded contrast first suggested. Finally, we flag learning from quantum experiments, whose classical sample-complexity lower bound is an unconditional theorem, as the one adjacent frontier where a quantum advantage is provable but not yet bridged to chemistry.
Parameterised quantum circuits are commonly assessed using measures such as expressibility, gradient behaviour, and entanglement. While useful, these measures do not indicate whether a circuit respects the symmetry it was designed to respect. This is especially important in equivariant quantum machine learning, where symmetry is central to the model. We introduce PsiAudit, an open-source Python toolkit for auditing symmetry-aware quantum neural network ansätze before training. Given an ansatz, a target symmetry, and a state trajectory, PsiAudit reports how the circuit occupies symmetry sectors, maintains coherence between them, fluctuates across the trajectory, and complies with the target symmetry. These outputs are combined into a configurable dashboard-style summary. PsiAudit supports phase, spin, and permutation symmetries, with the permutation audit implemented using Hamming-weight orbits. Tests on five ansatz families, across twenty random seeds and four to eight qubits, show, in the tested setting, that PsiAudit can identify inactive equivariant circuits, recover structure when multiple symmetry sectors are activated, and distinguish ansätze that appear similar under standard diagnostics. The toolkit also includes a unitary-level compliance check, reproducible examples, and a notebook for regenerating the reported results.
Hassan Ugail, Newton Howard· PLoS ONE· 0 citations
In this work, we investigate the application of Machine Learning (ML) algorithms to the identification and quantitative characterization of quantum entanglement in polarization-entangled photon pairs. The analysis is based on simulated symmetric, informationally complete, positive operator-valued measure (SIC-POVM) measurement data, where each two-qubit state is represented by a 16-dimensional measurement vector corresponding to experimentally accessible coincidence counts. The generated SIC-POVM measurement data include Poissonian shot noise. Several supervised ML algorithms, including Logistic Regression, k-Nearest Neighbors, Decision Trees, Support Vector Machines, and Random Forests, are applied to the classification of separable and entangled states directly from raw measurement data, without explicit density matrix reconstruction or the use of conventional separability criteria. The study additionally explores clustering methods and nonlinear regression techniques for estimating continuous entanglement measures. The obtained results demonstrate that ML methods can achieve very high classification accuracy, even under extremely limited training conditions. These findings indicate that ML may provide an efficient alternative to conventional quantum-state analysis under simulated Poissonian noise conditions.
Artur Czerwinski, Maciej Wiśniewski, Paweł Moszczyński· Electronics· 0 citations
Extracting quantum information from a quantum state is a fundamental task of quantum computation, often requiring the estimation of many non-commuting observables under a finite measurement budget. For both near-term and early fault-tolerant settings, the measurement protocol must balance statistical efficiency against implementation resources such as circuit depth, connectivity, and entangling-gate count. Many existing strategies focus on two extremes: hardware-friendly product measurements with high sampling cost, and fully commuting measurements with deep circuits. Here we recast resource-constrained measurement design as a generative learning problem. We introduce FlowMeas, which uses a generative flow network to directly sample finite ensembles of shallow Clifford measurement circuits subject to a prescribed shot budget and hardware constraints. At zero entangling depth, FlowMeas learns qubit-wise commuting measurement schedules and already matches or improves leading product-measurement methods on nearly all molecular benchmarks. Allowing one or two entangling gate layers yields further reductions in energy estimation error of up to $27\%$ relative to the strongest state-independent product-measurement baseline. The learned policy can also be reused across related Hamiltonians, substantially accelerating retraining along a molecular potential-energy surface. We further obtain results for molecular Hamiltonians with up to 20 qubits and apply the framework to a compactly encoded 54-qubit interacting fermionic model, extending the demonstrated scale beyond prior molecular benchmarks. These results establish generative learning as a flexible and unified framework for quantum measurement design under practical resource constraints.
Jun Dai, O. Nahman-Lévesque, Guillaume Rabusseau et al.· 0 citations