Training variational quantum models requires choosing between parameter-shift gradients, which are exact but cost $O(P)$ forward evaluations, and simultaneous perturbation stochastic approximation (SPSA), which uses only two samples but produces high-variance estimates that can degrade optimisation on small supervised tasks. Whether the cheap gradient is usable depends on the variance that results from different choices of the SPSA perturbation scale, learning rate, and gain-decay schedule. We varied those quantities across a broad grid on a 6-qubit, 60-parameter QNLI classifier and compared the best configurations to parameter-shift AdamW and BuresQNG. AdamW-style SPSA with $c_0=0.01$, $\eta=0.10$, $\gamma=0.10$ reached $55\% \pm 11\%$ test accuracy, improving over the default configuration ($49\% \pm 6\%$) but remaining 16-19 percentage points below the parameter-shift baselines because the two-sample SPSA gradient estimate has too much variance for reliable optimisation of 60 parameters in 40 epochs. Classical-gain SPSA and Bures-preconditioned SPSA performed worse, at $51\%$ and $46\%$ respectively. Bures-preconditioning a noisy two-sample SPSA gradient amplifies perturbation noise.
Training the variational angles of the Quantum Approximate Optimization Algorithm once on a small instance and reusing them on larger ones, known as parameter transfer, is the standard route past the exact-simulation wall. Existing literature explains its success almost entirely through structural similarity. We identify a new, independent axis that governs transfer whenever constraints are encoded as penalties: the trained angles memorize the penalty weight $\lambda$ of their training instance. For any scalarized cost function with an integer-valued violation count, we prove that at arbitrary fixed QAOA angles $(\beta,\gamma)$ of depth $p$, the probability mass $F(\lambda)$ on the feasible subspace is a finite real trigonometric polynomial in $\lambda$ whose angular frequencies lie on an integer lattice generated by the trained $\gamma$'s. Three consequences follow immediately: transfer feasibility is a resonance peaked where the deployment penalty matches the training penalty; the resonance width scales as $1/(v_{max}\sum_k|\gamma_k|)$, so low-$|\gamma|$ angle sets are systematically more transferable; and the curve exhibits revival peaks at spacings $2\pi/\gamma_k$. We confirm all three predictions by exact statevector experiments on a 20-qubit multi-user resource-allocation QUBO. The theorem is independent of how the angles were obtained and applies to any integer-penalty QUBO, recasting a widely reported failure mode of penalty-based QAOA as deterministic, predictable phase interference rather than an energetic tuning problem.
The results indicate that symmetry compilation concentrates the expressive power of NQS on states relevant to the target problem, thereby reducing model size and training cost without sacrificing accuracy.
Turbasu Chatterjee, M. Sajjan, Songbo Xie et al.· 0 citations
In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid training, bridging the energy-based formulation and the implementation-level quantum computation. Unlike prior comparisons, our evaluation enforces symmetric hyperparameter optimisation: classical and quantum-specific hyperparameters receive an equally thorough grid search across thirteen structured experiments. We test on two data classes, a Gaussian-process dataset (GP) generated with real financial data and the input-driven NARMA-10 nonlinear benchmark. Across both regimes we find no systematic evidence of a quantum advantage at the available sample size: no quantum architecture improves on the best classical baseline. The fully quantum QQRBM and QFeatureQRBM are significantly worse, whereas the hybrid QCRBM is statistically indistinguishable from the strongest classical CRBM on both datasets. A power analysis bounds this null result: at n = 12 only medium-to-large effects are detectable, so small advantages cannot be excluded. An iso-parameter (matched-budget) comparison reaches the same conclusion: the classical CRBM is lowest at three of the four budgets and no CRBM-vs-QCRBM difference is significant at any budget.
Gerhard Hellstern, Danyal Maheshwari, Martin Zaefferer et al.· 0 citations
This work examines when structured long-range connectivity provides a useful resource, focusing on sparse power-of-two (PWR2) coupling graphs, and identifies circuit geometry and qubit reconfigurability as task-dependent resources for variational algorithms.
Helene M. Losl, Aydin Deger, Andrew J. Daley· 0 citations
This work presents spectral Born machines, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis, and suggests that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes.
Austin L. Huang, William Maxwell, Vasilis Belis et al.· 3 citations
Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies, as existing Lindblad estimation methods are typically limited to small system sizes due to the computational complexity of repeatedly solving the Lindblad equation during optimization. Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a stochastic simulation method, the Tensor Jump Method (TJM), with gradient-free optimization of a least-squares cost-function defined on time series of local-observable expectation values. We demonstrate the approach on two noise models in the Ising model: a site-resolved (local) model, in which independent dissipation rates are learned for each site up to $N_{\mathrm{site}}=16$, and a spatially homogeneous (global) model with only seven parameters, scaled to $N_{\mathrm{site}}=160$ sites.We complement these numerical results with a series of exact, provable guarantees: the Frobenius variance of the TJM density-matrix estimator is shown to equal $(1-\mathrm{Tr}[\rho^2])/N_{\mathrm{traj}}$, an exact purity-based characterization of the stochastic estimation error; the corresponding purity evolution is proven to be monotonically non-increasing for Hermitian jump operators; and, under a finite covariance distance assumption, the standard deviation of the cost-function is shown to decrease with system size, so that fewer trajectories are needed to reach a fixed target accuracy as the system grows. Together, this combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices and for guiding future work on error mitigation and quantum error correction.
A. R. Ramos Ramos, Maximilian Fröhlich, Aaron Sander et al.· 0 citations
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