quant-phOct 5, 2026
SaveQuantum data loading from the learned shared structure of real signals
Organizations: Department of Computer Science Technology and Computation, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain
Abstract
Preparing quantum states from classical data can cost more than the computation they serve; most loaders tailor a circuit to each input. Here we show that the signals of a real dataset share structure that can be learned once and reused. Our quantum-native loader learns a low-dimensional description of a dataset and prepares every signal with one fixed circuit set by a few numbers. Across seven views of five public datasets it meets the targets of the strongest structured loader at equal gate cost with several times fewer numbers per signal. These numbers can be inferred from a random subset: in a preregistered blind replication the subset needed to come within ten per cent of full-signal accuracy stayed constant within a prespecified margin as signals grew sixteenfold, whereas the structured loader needed ever more. It declines what it cannot represent, covering fewer cases than that baseline and no electrocardiogram.
Figures & tables
Figure 1 : A learned family turns a window into a few coordinates of one fixed circuit. a , Loading pipeline. A shared Walsh support (top) takes free coefficients from the complete window; QNL (bottom) takes latent coordinates and evaluates the coefficients through the affine decoder . Both paths end in one circuit whose topology is fixed for the whole dataset and whose phase gadgets differ between windows only in their angles, so both circuits receive one coefficient per support term: what differs is how many numbers each window has to supply. The counts shown are means over the deployed models at the central target fidelity (99.50%). b , Why that interface is narrower. The same seven windows, in the plane of two Walsh coefficients. One fixed axis leaves a large residual on every window (left, dashed); one direction fitted to the family leaves a small one (right), so fewer coordinates describe the same windows. The fitted directions are constrained to lie in a physically realizable Walsh support, which is what distinguishes them from an unconstrained principal component 30 . c , Protocol. The subspace, the support and the circuit are learned on FIT; VALIDATION applies the deployment contract and the method abstains, and is priced at a declared fallback, when that contract is not met; TEST is materialised once, after every selection has been frozen. d , Partial observation. From the observed positions alone the least-squares projection returns the coordinates, and these already determine the circuit angles through ; the complete window is reconstructed only to score the error against the held-out window, never as a deployment object.
Figure 2 : One shared decoder describes a window with a fraction of the numbers a Walsh support needs. a , State-preparation error on TEST against the number of sample-specific degrees of freedom exposed by each method, with no target fidelity imposed. Points are means over the cases of the main campaign that have a model at that count; no error bars are drawn. Where QNL has fewer cases than the baselines its is printed beside the point, because a case whose selected latent is smaller cannot be evaluated at a larger one. The exact diagonal has zero error and is drawn on the lower edge at numbers. b , Ratio of the free coefficients the searched shared Walsh support needs to QNL-pruned’s , per dataset, at the central target fidelity (99.50%), over the cases where both deploy; violins show the distribution over cases and seeds, bars the per-dataset median, and the title the geometric mean over all datasets (5.25). PTB-XL is absent because QNL-pruned deploys on none of its cases (Fig. 6 a).
Figure 3 : The circuit is no more expensive than the strongest Walsh baseline and far cheaper than per-sample and exact loaders. a , Paired ratio of two-qubit gate count, QNL-pruned over the searched shared Walsh support, one row per dataset and window length , one panel per target fidelity. Points are geometric means over the seeds in which both methods deploy; bars are 95% Student intervals taken on the log scale. Cells with fewer than three paired cases are drawn as open points without an interval. The shaded band is the declared equivalence band and the line is parity. PTB-XL has no row because QNL-pruned deploys on none of its cases. b , Paired CX ratio of QNL-pruned to the per-sample Walsh support with a common , with an adaptive , and to the exact diagonal, per target fidelity; bars are geometric means over paired cases and whiskers 95% intervals on the log scale. The range of over the four fidelities is given in the legend. Aggregates are never pooled across fidelities.
| target fidelity | method | deployed | CX | depth | numbers per window | TEST fidelity | |
|---|---|---|---|---|---|---|---|
| 99.00% | QNL-pruned | 120/140 | 61.4 | 109.8 | 57.6 | 13.8 | 0.98675 |
| 99.00% | QNL-v5 (ablation) | 120/140 | 69.4 | 123.2 | 66.0 | 13.8 | 0.98810 |
| 99.00% | mean only | 0/140 | – | – | – | – | – |
| 99.00% | order 1 | 0/140 | – | – | – | – | – |
| 99.00% | shared static Walsh | 134/140 | 85.4 | 155.8 | 79.6 | 79.6 | 0.98988 |
| 99.00% | shared static Walsh (searched) | 134/140 | 83.0 | 152.3 | 79.2 | 79.2 | 0.98901 |
Table 1 : Resources per target fidelity. For each method, the number of the 140 cases where it deployed, and the mean two-qubit gate count (CX), circuit depth, number of physical Walsh terms ( ), sample-specific numbers per window and TEST fidelity over the cases where it deployed. Means are taken over each method’s own deployed cases and are therefore not paired comparisons; coverage is the first column. mean only and order 1 deploy on no case.
Figure 4 : Shared supports scale sublinearly with window length, and their saving over exact loading survives gate noise. a , Two-qubit gate count against window length , both axes logarithmic, at the central target fidelity (99.50%); points are geometric means over each method’s deployed cases and the upper axis gives the qubit count . The fitted exponent of and its 95% interval are given in the legend for each method. The point uses 17 of 18 runs; PTB-XL has no view. b , Estimated total fidelity against two-qubit gate error at the central target, for QNL-pruned, the searched shared Walsh support and the exact diagonal, using each method’s mean gate count and mean TEST error over the same cases, those where all three deploy; their number is given in the panel title and each method’s mean CX in the legend. This panel is an analytic estimate, not a simulation. Dotted lines mark the gate errors declared by the protocol.
Figure 5 : With random observations, the number of positions QNL needs to approach its full-window accuracy is constant within a prespecified margin as the window grows, while the shared Walsh support’s grows. a , Preregistered blind replication (Supplementary Note 5): the number of randomly observed positions each method needs for its error to come within 10% of its own error with the whole window, against the window length , both axes logarithmic; selected on VALIDATION from recordings never used as TEST before, central target fidelity (99.50%). Points are geometric means over the cases where both methods deploy; lines are the mean per-unit slopes, given in the legend with the 90% interval for QNL-pruned (the equivalence test, margin ) and the 95% interval for the Walsh support. The dotted line is , the whole window. This is not the number of positions needed to meet . b , c , Exploratory context, from the experiment that suggested the question: mean on TEST against the observed fraction , random mask (b) and one contiguous gap (c), central target fidelity; the dashed line is . Paired cases only: within each fraction every method is averaged over the cases where all of them deployed ( , in the legend); intervals are in Supplementary Table 5. For QNL, already determines the fixed circuit; the whole window is reconstructed only to score error. The matched- control is the shared static Walsh construction truncated to QNL’s number of effective unknowns.
Figure 6 : Where the method stops working. a , Coverage of each method over the 140 cases of the main campaign, one bar per target fidelity from 99.00% to 99.75%. The coloured part is the share deployed; the hatched parts above it are abstentions by declared cause. b , Expected two-qubit gate count per case at the central target fidelity (99.50%), with each abstention priced at the declared fallback policy: exact diagonal (plain) or searched shared Walsh support backed by the exact diagonal (hatched). Bars are arithmetic means over the 140 cases, since an expected cost is an expectation; is given in the legend. c , Negative control: deployments on 28 surrogate runs (seven views at , four target fidelities) whose windows were permuted in place. The black tick is the lower bound on the count restricted to non-trivial windows; the per-window TEST errors needed to compute it exactly are not in the records. d , Extended latent grid ( ) on the cases that abstained for accuracy, by dataset and target fidelity: 13 of 98 rescued. Reported as the ablation’s own result and never folded into the coverage in a .