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When Do Entangling Gates Add Predictive Signal? A Preregistered Falsification Study for Hybrid Quantum-Classical Combinatorial Optimization

David Vesterlund

Published Oct 5, 2026• 0 citations
Publisher

Abstract

Abstract \small\noindent Choosing the best heuristic for a combinatorial optimization instance depends on landscape structure that cheap graph descriptors capture only partly. We test whether a small quantum circuit, used as a fixed feature map, adds predictive signal about solver performance beyond such descriptors. Graphs are spectrally compressed to eight supernodes and encoded in a single-layer circuit of $R_Y$ rotations and $R_{XX}$ entangling gates; eight pooled statistics computed from $Z$- and $X$-basis expectation values feed a classical ridge readout. In a preregistered protocol on 10{,}000 simulated graphs the features add $\dR = 0.0208$ (Nadeau--Bengio corrected 95\% CI $[0.0202, 0.0214]$, permutation $p = 1/1001 \approx 0.001$) over twelve descriptors. They exceed random-projection and random-Fourier controls; a paired test does not separate them from a random $\tanh$ reservoir ($p = 0.22$). \textbf{However, flexible classical models with access to the same compressed graph input $(h,J)$---Random Forest ($\dR = 0.179$) and XGBoost ($\dR = 0.145$)---dramatically exceed Q1, as does a simple linear ridge ($\dR = 0.030$). The quantum feature map does not provide superior predictive signal beyond what classical models extract from the same input.} Removing the entangling gates lowers the gain ($p<10^{-7}$), and the Z-basis component of the gain peaks at half entangling strength (exploratory), consistent with a closed-form phase-accumulation mechanism. The qualitative conclusion $\dR > 0$ is robust across solver budgets $\{25, 50, 100\}$. On a 20-qubit trapped-ion processor with a matching native gate set, hardware features reproduce simulated ones (mean $r = 0.81$, 200 shots); at $n = 250$ a simulation-trained readout applied to hardware features gives $\dR = +0.016$ (calibrated), and the Q1$-$Q0 difference ($+0.310$, calibrated) is driven by Q0 collapsing under noise rather than entanglement adding information, as confirmed by a noise-augmented readout control. We propose a quantum-centric supercomputing (QCSC) architecture that \emph{projects} a $2\times$ QPU-time reduction through graph packing. \textbf{We claim no quantum advantage.} The contribution is a falsification-tested, mechanistically interpretable, hardware-portable feature map---not a superior predictor. The quantum features do not improve practical solver selection (45.1\% accuracy with or without $Q$). The signal does not generalize to most out-of-distribution graph families under the corrected protocol.

DOI
10.21203/rs.3.rs-11192113/v1

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Abstract We introduce a novel hybrid quantum–classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual variational parameter update strategies, efficient parametric compilation, automated error suppression during hardware execution, and scalable O( n ) classical post-processing to correct for bitflip errors. Without this integrated approach, we show that standard circuit execution at scale produces output indistinguishable from random sampling, establishing the necessity of each pipeline component. We benchmark the method on IBM superconducting quantum computers for several optimization problems drawn from NP-hard problem classes, where the optimization is conducted on hardware with no use of classical simulation or prior knowledge of the solution. For Max-Cut on random regular graphs with topologies not matched to device connectivity, the method achieves approximation ratios (AR) of 100% for unweighted 3-regular graphs up to 156 nodes, weighted regular graphs up to 80 nodes, and weighted 7-regular graphs up 50 nodes. Applied to higher-order binary optimization, the method finds the ground state energy of 127- and 156-qubit spin-glass models matched to device topology with linear, quadratic, and cubic interaction terms, achieving ARs of at least 99.5% across all instances tested. The method consistently outperforms a classical local solver across all problems. Where published results on identical problem instances are available, our method demonstrates competitive or superior performance. These results demonstrate that an appropriately engineered variational approach enables gate-model quantum computers to produce high-quality solutions for binary optimization problems drawn from NP-hard problem classes at the 156-qubit scale, where naïve implementations are insufficient for good performance.
The performance of the Variational Quantum Eigen-solver (VQE) is promising compared to other quantum algorithms, but also depends significantly on the appropriate design of the underlying quantum circuit. Recent research by Bowles, Ahmend & Schuld, 2024 [1] raises questions about the effectiveness of entanglement in circuits for quantum machine learning algorithms. In our paper we want to address questions about the effectiveness of state preparation via Hadamard gates and entanglement via CNOT gates in the realm of quantum optimisation. We have constructed a total of eight different circuits, varying in implementation details, solving a total of 100 randomly generated MaxCut problems. Our results show no improvement with Hadamard gates applied at the beginning of the circuits. Furthermore, also entanglement shows no positive effect on the solution quality in our small scale experiments. In contrast, the investigated circuits that used entanglement generally showed lower, as well as deteriorating results when the number of circuit layers is increased. Based on our results, we hypothesise that entanglement can play a coordinating role, such that changes in individual parameters are distributed across multiple qubits in quantum circuits, but that this positive effect can quickly be overdosed and turned negative. The verification of this hypothesis represents a challenge for future research and can have a considerable influence on the development of new hybrid algorithms.
Variational quantum classifiers (VQCs) are often reported to perform poorly on biomedical tabular data, but such conclusions depend on the encoding circuit, the training budget, and the comparison protocol. Methods. We compared 4-qubit VQCs, a quantum-kernel SVM (QSVM), a majority-class control, and tuned classical models (on four PCA features and on all features) on Wisconsin breast cancer (n = 569), Coimbra biomarkers (n = 116), Golub leukemia gene expression (n = 72, 7,129 genes), and SEER breast-cancer registry data (n = 4,024; 15% deaths). All models were evaluated on identical blocks of 5-fold × 5-seed stratified cross-validation with preprocessing fitted on training folds, nested tuning, and Nadeau–Bengio-corrected inference with Holm correction. Trained classifiers were also evaluated on three IBM Quantum devices. Results. On the three small datasets, a VQC with the conventional two-repetition ZZ feature map was close to chance (accuracy 0.688, 0.594, 0.509), whereas a product (Z) feature map reached 0.900, 0.797, and 0.658; at matched repetition counts the Z-minus-ZZ gap was +0.12 to +0.21 and, after Holm correction, significant on Wisconsin only. More evaluations (up to 1,500) and six initializations did not close the ZZ deficit on Wisconsin. With the encoding chosen by inner cross-validation, the VQC exceeded the majority control on Wisconsin and Golub and stayed below classical models on Wisconsin and in several Golub contrasts. No statistically significant difference was detected between the encoding-selected VQC and the classical baselines on Coimbra, or between the Z-map QSVM and PCA-4 classical models; Bayesian equivalence analysis supported practical equivalence only for the QSVM on Wisconsin. On SEER the encoding mattered little: the VQC exceeded the majority control in balanced accuracy (0.548 versus 0.500) but ranked patients worse than logistic regression and random forest (ROC-AUC 0.678 versus 0.745 and 0.733). Full-feature classical models were strongest overall. On hardware (class-balanced test subsets, not natural-prevalence performance), accuracy relative to noise-free simulation changed by −0.071 to +0.048 per run (pooled ibm_fez, Wisconsin: −0.024, 95% CI −0.060 to +0.008), using 5.5 QPU-minutes. Conclusions. Under a fixed training budget, encoding choice was associated with large differences in VQC accuracy on small datasets, so single-encoding negative results should not be generalized; because the Z and ZZ maps also differ in entanglement structure, we do not attribute the gap to encoding alone. No quantum advantage was observed.
Abstract An active area of investigation in the search for quantum advantage is quantum machine learning. Quantum machine learning, and parameterized quantum circuits in a hybrid quantum-classical setup in particular, could bring advancements in accuracy by utilizing the high dimensionality of the Hilbert space as feature space. But is the ability of a quantum circuit to uniformly address the Hilbert space a good indicator of classification accuracy? In our work, we use methods and quantifications from prior art to perform a numerical study in order to evaluate the level of correlation. We find a moderate to strong correlation between the ability of the circuit to uniformly address the Hilbert space and the achieved classification accuracy for circuits that entail a single embedding layer followed by 1 or 2 circuit designs. This is based on our study encompassing 19 circuits in both 1- and 2-layer configurations, evaluated on 9 datasets of increasing difficulty. We also evaluate the correlation between entangling capability and classification accuracy in a similar setup, and find a weak correlation. Future work will focus on evaluating if this holds for different circuit designs.
Abstract Quantum kernel results are often reported without holding the input representation, training sample, tuning budget and temporal evaluation protocol fixed against a matched classical kernel. This pre-specified, protocol-locked falsification study uses the Elliptic++ transaction tables (203,769 transactions, 49 time steps) under a locked temporal split (training steps 1–24, validation 25–29, test 30–49 in 4 locked windows). The primary metric is pooled Recall@5%. A frozen full-dimensional gradient-boosting model reached 0.381, and every model, including this one, collapsed in the final window. Graph structure and selective reranking were tested first and falsified. Compressing 182 features to 4, 6 and 8 principal components retained 34%, 43% and 51% of the variance and 64%, 50% and 33% of the full-dimensional model’s pooled Recall@5%. In the primary, default-bandwidth analysis, an entangling fidelity quantum kernel was below the strongest matched classical kernel at 4, 6 and 8 qubits (pooled Recall@5% differences −0.078, −0.203 and −0.146). In a secondary, post hoc bandwidth correction, explicit scale tuning raised the entangling kernel’s Recall@5% by 0.070, 0.121 and 0.109; the corrected kernel remained below the strongest matched classical kernel at 6 and 8 qubits and was statistically unresolved at 4 qubits. The selected scale lay at the lower boundary of the tested grid, and the apparent effect of entanglement depended on bandwidth. No repeatable predictive benefit of the quantum kernel over matched classical kernels was observed in the tested setting; the findings do not extend beyond this dataset, protocol, representation, feature-map family, sample size and bandwidth range.
Near-term variational classifiers incur substantial error and latency from two-qubit gates, yet practitioners often assume that additional entangling depth is the default route to higher accuracy. This work studies Optimal Quantum Measurement Decoding (OQMD): optimizing how quantum outcomes are mapped to classical labels by training a readout layer before measurement, jointly with the variational circuit, without adding CNOTs. Experiments use trainable triple single-qubit rotations as one concrete, hardware-native realization of OQMD; other single-qubit parametrizations fit the same classical outer loop. On the Iris benchmark with a 30-point stratified test split, the best observed 0-CNOT configuration with OQMD reaches 83.33\% accuracy, with a 96\% at 9 CNOTs, exceeding the best 18-CNOT controls (56.67\%) and the best 18-CNOT configuration with OQMD (66.67\%) under a common protocol. A six-point CNOT-depth series from 0 to 18 (fixed optimizer, iteration budget, random-seed count, and ZXZ readout) shows that the highest raw scores need not occur at the largest template, so aggregate complexity is not summarized by CNOT count alone. Because run-level accuracies are discrete and non-Gaussian, we emphasize best-observed scores and, where a global comparison of pooled runs is required, Mann--Whitney UUU tests rather than parametric tests on means. Across architectures, OQMD shows statistically consistent but magnitude-dependent gains: large peak lifts on minimal circuits coexist with a small pooled mean shift on complex 18-CNOT runs (p≈0.03p\approx 0.03p≈0.03) that is not ``universal'' in the sense of uniformly large practical effects.%