quantum algorithm engineers

Abstract: Compact quantum neural networks have been explored for cloud-cover parameterization, but their predictive value depends on how physical knowledge is incorporated and which classical models provide the reference. We investigate an offline residual formulation that retains a fitted \XR\ cloud-cover estimate and learns a correction to its logit in transformed target space. Using released ICON/DYAMOND-derived data, we compare ten model variants in six- and eight-input settings, with three matched replicates and 10,000 training samples per replicate. All quantum circuits use local Z readout and noiseless exact expectation values. Under a common 30-epoch protocol, residual prediction reduced physical-space test mean squared error relative to direct QNN prediction by 54.3\% and 38.8\% for six-input XYZ and ZZXY circuits, and by 49.2\% and 38.9\% for their eight-input versions. Residual QNNs also outperformed the selected compact residual multilayer perceptron in every paired replicate. A larger, longer-trained Grundner-Q1 adaptation nevertheless achieved lower error: residual Q1 reached mean MSEs of 0.00778 and 0.00791, compared with 0.01124 and 0.01082 for residual XYZ. The results support residual prediction for compact simulated QNNs within the tested budget and establish a clear boundary set by stronger classical references. They do not establish computational quantum advantage or online climate-model skill.

Abstract: Understanding generalization is essential for assessing the practical viability of quantum machine learning. In many applications, quantum models operate on classical data that must first be encoded into quantum states, making the encoding part of the effective hypothesis class. We develop a margin-based generalization framework for this setting, covering both fixed and trainable quantum data encodings. For fixed encodings, the existing margin bound transfers unchanged. For trainable encodings, we derive a bound using a two-scale covering argument that combines the original margin-dependent term with an additive encoding-capacity term of order $\tilde O(\sqrt{L/m})$, where $L$ is the number of trainable encoding parameters and $m$ is the training-sample size. Across 19,440 simulated training runs spanning various image datasets, circuit architectures, and optimization settings, the inverse margin performs best among five baseline and two bound-derived complexity measures under conditional-independence and 90th-percentile sign-error criteria, within bootstrap uncertainty. These results provide a unified margin-based view of generalization in quantum machine learning with classical data.

Abstract: In order to execute quantum algorithms on bosonic quantum computers, it is necessary to encode their inputs into a desired target quantum state, with a process called state preparation. In real settings, state preparation methods operate in stochastic scenarios, where the prepared state is represented as a mixed state, that is a probabilistic ensemble of pure states. Therefore, existing state preparation methods optimize a variational ansatz by averaging over all possible sequences of photon loss events contained in the prepared ensemble, yielding an output state which approximates the desired target with a certain average fidelity. Such an approach, however, does not take into account directly the distribution of fidelities across states in the ensemble. In this work, we aim to maximize the fidelity of only a subset of pure states sampled from the prepared ensemble, at the cost of reducing the average fidelity overall. This trade-off is relevant when the goal is to obtain high-fidelity states with a certain probability, rather than maximizing the average fidelity of the prepared ensemble. We borrow and adapt objective functions from risk-sensitive optimization, a framework that optimizes specific characteristics of a distribution rather than only its expectation, and that has been successfully applied in Reinforcement Learning. In the considered experimental settings, our results show that the infidelities of some pure states in the prepared ensemble can be reduced by up to four orders of magnitude when using risk-seeking objectives, compared to those achieved using the standard optimization of the average fidelity. Furthermore, we show that it is possible to control the trade-off between the probability of obtaining high-fidelity states and the lowest infidelity threshold reached, providing the flexibility to select the operating point that best suits a certain application.

Abstract: Which execution details must a quantum computation retain, and to what precision, to support a declared comparison? We define a sufficient record by the largest Hellinger distance between outcome laws that share it. Our main result is a circuit-derived certificate for continuous recording precision: independent channel-mixture probabilities enter through the affinity of latent noise flags, while coherent rotation differences enter through conditional quantum fidelity. Their joint composition bounds whole record cells without simulating their outcome distributions. For four-qubit QAOA at depth one, a 13-bit comparison record guarantees distance below 0.05 throughout a declared continuous noise box, uniformly over programmed angles when comparisons hold the logical task fixed. A construction with observable noise flags attains the general bound. Exact tensorization of Hellinger affinity connects recording precision to the length of a future measurement transcript. On finite context classes, separation witnesses certify minimum-cost field retention; a four-field record is the unique minimum for 28 archived QAOA instances. Fresh six-qubit processor measurements establish different minimum label counts at one common tolerance: two labels are necessary and sufficient for raw laws, while one suffices after a fixed decoder for a synthetic image-segmentation task. These hardware conclusions are conditional on stationary independent shots and remain distinct from the analytic channel certificate. Shared task definitions and evidential archives are retained separately. The framework specifies which execution distinctions matter, how precisely to record them, and what evidence supports the resulting agreement guarantee.

Abstract: We study a Continuous-Variable Quantum Approximate Optimization Algorithm (CV-QAOA) for high-dimensional continuous optimization. Our formulation extends an earlier CV-QAOA proposal with a variationally optimized initial state and recovers the convergence guarantees of Quantum Hamiltonian Descent (QHD) in the high-depth limit. We prove rigorous performance guarantees of CV-QAOA on several families of cost functions. First, we show $d$-step CV-QAOA minimizes any $d$-dimensional strictly convex quadratic function with $2d$ quantum queries to the cost function. We then analyze a family of nonconvex "Rotated Double Well" (RDW) functions with $2^d$ local minima introduced by arXiv:2311.00811. While prior work showed QHD reaches its global minimum with $\tilde O(d^3)$ queries, we prove that 1-step CV-QAOA solves RDW with just two quantum queries. Although general-purpose classical solvers need superpolynomial time for RDW and structure-awareness can reduce the cost to polynomial time, we show that the 1-step CV-QAOA protocol can be efficiently dequantized, and that a gradient-aligned line search succeeds with $O(d)$ queries, nearly matching the information-theoretic $Ω(d/\log d)$ query lower bound. To move beyond the dequantizable regime, we introduce a ``Rotated Square Well'' (RSW) problem, whose globally flat landscape suppresses useful local gradient information. For this family, we show that an adiabatic evolution simulated by CV-QAOA can reach the global minimum using $d^{o(1)}$ queries. On the other hand, any classical algorithm that learn the hidden rotation in RSW provably requires $Ω(d^2/\log d)$ queries, a bound we nearly match with an explicit $Θ(d^2\log d)$-query classical algorithm.Numerical simulations on deflected corrugated spring and Easom functions illustrate the promising performance of CV-QAOA on more general problems.

Abstract: An analog device implements a local Hamiltonian H, but a polynomial P (H) is in general not local, so the device cannot implement it. We carry P (H), to any prescribed accuracy, as the action of a single time-independent local Hamiltonian on an explicitly described invariant subspace. Short chains of ancilla qubits are attached to H. A chain of 2m sites has a unique isolated eigenvalue that is an analytic function of the input vanishing to order exactly 2m, because the input must cross the chain and come back before it can shift the energy at the far end. Chains of different lengths therefore form a triangular family, and a weighted sum of them reproduces a prescribed polynomial term by term. Even chains give the even part and odd chains the odd part, so any polynomial is reached. We prove uniqueness, analyticity and coefficient bounds uniform in the chain length for inputs H of norm below any r < 1. Where the circuit model pays degree 2l in 2l sequential oracle calls, the result here is one Hamiltonian of locality two more than that of H, which pays the degree in O(l^2 + log2^(1/eps)) ancillas and in energy scale. As an application we filter a marked eigenstate of a local Hamiltonian. Composing a synthesised square along the Chebyshev doubling identity works, but its energy scale grows quasi-polynomially with the degree. Iterating instead the exact eigenvalue branch of the two-site chain k times gives a filter on k + 1 ancilla qubits whose error decays geometrically in k, at an energy scale polynomial in the inverse passband width and independent of k, the locality growing by one per stage. In adiabatic optimisation with a rank-one driver, the construction replaces that non-local driver, by a Hamiltonian with O(log n) ancillas and O(log n)- body terms, at an energy scale polynomial in n. Simulations including every ancilla reproduce the spectrum of the ideal algorithm.

Abstract: Quantum speed-ups have been obtained for many fundamental graph problems, including most variants of matching. A notable exception, however, is the maximum-weight perfect matching (MWPM) problem in general graphs with integer edge weights, which is arguably the most challenging variant of matching. We present a quantum algorithm for MWPM in general graphs that runs in \( \widetilde{O}(n m^{2/3}\log W) \) time, where $W$ is an upper bound on the magnitude of the edge weights. This is an improvement over the best known classical combinatorial bound of \( \widetilde{O}(m\sqrt n \log W) \) in the dense regime, where $m\ge n^{3/2}$. To the best of our knowledge, this is the first quantum algorithm to obtain an asymptotic improvement over the best classical combinatorial algorithm for the MWPM problem in general graphs. The running time of our method accounts for QRAM initialization and access overheads up to polylogarithmic factors, as well as all classical updates to the data structures. At a high level, our algorithm is based on a classical framework due to Duan, Pettie, and Su, but our algorithm requires replacing certain classical tasks with quantum methods, alternative analysis of classical procedures, and the use of alternative data structures that can be implemented effectively in the QRAM model.

Abstract: Fingerprint recognition is a widely deployed biometric, but supervised training requires large labeled enrollment sets. Self-supervised learning (SSL) removes this requirement, and hybrid quantum-classical models have been proposed to enrich the learned representations. Prior quantum SSL studies consider a single contrastive objective, so it is unclear whether reported benefits depend on the objective or can be attributed to the quantum circuit. We insert the QuFeX quantum feature-extraction module into three SSL frameworks, the contrastive SimCLR and MoCo v2 and the non-contrastive BYOL, and compare each hybrid with its classical counterpart at matched representation width (8 features, equal to 8 qubits) on the SOCOFing fingerprint dataset, with a CIFAR-10 control, using k-nearest-neighbor identification on encoder features. In single-run experiments the hybrid scores clearly higher for both contrastive objectives, whereas for BYOL a multi-seed analysis shows no reliable difference, suggesting that any benefit depends on the SSL objective. A hardware-efficient circuit (QNet) does not show the same gain. We examine whether the gains can be attributed to the quantum circuit, considering circuit architecture, trainable parameter count, nonlinearity, and the classical simulability of 8-qubit circuits.

Abstract: We study whether the coordinate dependence of the improved Self-Organizing Migrating Algorithm (iSOMA) can be reduced while retaining its inexpensive leader-directed migration mechanism. We introduce iSOMA-AR, which learns a basis from successful migration displacements and selectively applies the standard perturbation mask in that basis. On the complete noiseless BBOB suite, iSOMA- AR significantly outperformed baseline iSOMA across matched conditions, with the largest gains on geometrically difficult landscapes. A targeted ablation shows that the learned orientation is beneficial on a rotated ill-conditioned landscape and that moderate changes of the gate threshold and rotation cap preserve the qualitative result. On CEC 2011 Real World Optimization Problems, iSOMA-AR outperformed iL-SHADE on most problems, although its advantage over baseline iSOMA was not statistically significant. A canonical-jSO rerun is reported as a post-hoc sensitivity check alongside the original jSO-derived comparator. On frustrated-spin variational quantum objectives, adaptive rotation improved most transverse-field conditions, while gains on the diagonal and anisotropic models were absent or selective. Under strong effective sampling noise, the SOMA variants were the most robust population-based methods in the comparison, but iSOMA-AR was not significantly better than baseline iSOMA. Repairing all-zero PRT masks greatly reduced repeated-point evaluations without changing endpoint quality significantly, making this implementation detail unlikely to explain the noise result. Overall, adaptive rotation is most useful on coordinate-sensitive deterministic problems, while the observed noise robustness appears to arise mainly from the underlying SOMA migration mechanism.

Abstract: Recent advances in quantum computing are opening new opportunities for computationally intensive decision problems. This paper studies how quantum computing can improve Monte Carlo tree search (MCTS) in the fixed-confidence setting, where the goal is to identify a near-optimal move in a given game tree with high probability while minimizing query complexity. We first formulate MCTS under a quantum oracle model. We then develop a quantum MCTS algorithm (QMCTS) that combines threshold-based elimination on the search tree with quantum Monte Carlo estimation to reduce the cost of evaluating stochastic leaf values. We establish an instance-dependent lower bound on the query complexity and derive a corresponding upper bound for QMCTS. The lower-bound analysis introduces a new quantum phase-testing result that may also be useful beyond MCTS. We validate the theoretical results through simulation experiments and further demonstrate the feasibility of QMCTS on real quantum hardware.

Abstract: Supervised approaches to quantum error mitigation learn a map from noisy circuit outputs to ideal ones, and therefore require the ideal outputs. Producing those ideal outputs demands noiseless classical simulation, whose cost grows exponentially with system size, so supervision is unavailable in exactly the regime where mitigation matters most. We ask whether cheap, individually unreliable signals drawn from circuit structure and hardware calibration can take the place of ideal labels. We assemble sixteen heuristic labeling functions (stabilizer and parity constraints, relaxation and readout characteristics, local depth, gate counts, and neighboring activity), reconcile their disagreements with a probabilistic label model, and read the resulting per-qubit error probabilities as a readout channel whose inverse mitigates the measured distribution. No ideal output enters the training path. On $147{,}000$ five-qubit circuits executed on two IBM devices, the method removes $24.3\%$ (Algiers) and $28.8\%$ (Hanoi) of the Kullback-Leibler divergence to the ideal distribution, against $15.4\%$ and $21.5\%$ for the strongest published analytical baseline, a margin that holds on both devices and lies far outside its bootstrap interval. Supervised neural models trained on ideal distributions remain stronger where such labels exist, and we quantify that gap rather than setting it aside; the method's claim is to the regime where they do not, since the labels they require cannot be computed for the circuits mitigation is needed for. The codes will be released shortly.

Abstract: How much memory is needed to retain the quantum speedup for collision finding? For a uniformly random function $f:[N]\to [N]$, the BHT algorithm finds a collision using $O(N^{1/3})$ queries and a quantumly accessible classical table containing $O(N^{1/3})$ input-output pairs, whereas a logarithmic-space Grover search uses $O(\sqrt N)$ queries. Determining the optimal query-space tradeoff between these extremes remains a major open problem. We resolve this equation within the class of label-symmetric algorithms, which treat the function $f$'s output labels as interchangeable. We prove that such algorithm that makes $T$ queries, uses $S$ qubits, and finds a collision in a uniformly random function $f:[M]\to [N]$ with constant probability satisfies $$T=Ω(N^{1/3}) \qquad\text{and}\qquad T^2S=Ω(N\log N).$$ For the setting where $M=N$, these bounds are matched by a space-efficient implementation of the BHT algorithm. As a consequence of our tradeoff, any label-symmetric algorithm for the search version of Element Distinctness on $f: [n] \to [n^2]$ must satisfy $$T=Ω(n^{2/3}) \qquad\text{and}\qquad T^2S=Ω(n^2\log n),$$ matching Ambainis's quantum walk. Thus, both tradeoffs are optimal within the class of label-symmetric algorithms. To prove these results, we develop a space-sensitive version of the compressed oracle technique. The compressed oracle records the information learned by the algorithm in an evolving superposition of databases. Using label symmetry and representation theory, we show that an algorithm using $S$ qubits can effectively retain information about only $O(S/\log N)$ collision-free database entries. Substituting this estimate into the compressed oracle technique yields the stated tradeoffs.

Abstract: We propose Open Autoresearch, a paradigm in which humans and AI agents publish evaluator-verified improvements to a public leaderboard. We instantiate it in ECDSA.Fail, optimizing reversible secp256k1 point-addition circuits, a bottleneck in Shor's algorithm for elliptic-curve cryptography. The benchmark minimizes the spacetime-inspired score $S=Q\times T$, where $Q$ is peak logical qubit width and $T$ is average executed Toffoli count. Participants reduced $S$ by 86.1%. At the data cutoff (26 July 2026), the best-scoring circuit uses 1,151 qubits and 1,299,453 average executed Toffoli gates, giving $Q\times T\approx1.496$ billion. This is more than 50% below Google's published point-addition score thresholds (arXiv:2603.28846), under different accounting conventions. Because the benchmark supplies one addend classically, we construct a coherent windowed-addition-compatible variant implementing the single-call interface required by windowed Shor. It uses 1,162 qubits and 1,684,161 average executed Toffoli gates. On 100,000 random inputs, its empirical success probability is $\hat{p}=0.99809$, giving $Q\times T/\hat{p}\approx1.961$ billion under an independently rerunnable per-call sensitivity model, not a full-Shor success estimate. Its qubit and Toffoli counts lie below Google's published thresholds and Schrottenloher's reported operating points (arXiv:2606.02235), although differing interfaces, accounting conventions, and validation scope preclude formal dominance. After the cutoff, the score was further reduced to 1.259 billion, while a separate low-width circuit reached 813 qubits. The public record shows AI agents complementing human judgment, providing evidence for open autoresearch on efficiently evaluable, machine-checkable objectives.

Abstract: Compressed quantum encodings aim to overcome hardware limitations towards tackling challenging problems at scale, with many classical variables mapped onto noncommuting observables of fewer qubits. Classically, relaxations such as the semidefinite program formulation of MaxCut trade solution quality for computational efficiency. By contrast, quantum relaxations based on compression can amplify the worst-case complexity of the problem being solved. We study quantum random access optimization (QRAO), a special case of the Pauli correlation encoding (PCE) framework that assigns up to three binary variables to the Pauli $X$, $Y$, and $Z$ observables of each qubit, with the packing choices determining the compressed Hamiltonian to be optimized. We identify explicit QRAO optimal energy promise problems complete for NP, StoqMA, and QMA, with inverse-polynomial promise gaps for the latter two. Our problem reductions preserve inverse-polynomial promise gaps without requiring gadgets or ancillas. For any prescribed packing, we show that weighted MaxCut instances compress, up to a known shift and rescaling, to arbitrary nonnegative-weight pairwise Pauli couplings allowed by the packing. For QRAO, using one aligned axis gives an NP-complete energy problem. Using two or three positive aligned Pauli axes generally gives QMA-complete problems, while their bipartite restrictions lie in StoqMA. We show that this computational hardness survives compilation and is practically relevant. Notably, this result applies directly to the current QRAO compiler implementation in Qiskit Optimization 0.7.0, confirming our hardness results are not artifacts of artificial or contrived packing rules. Altogether our results identify worst-case complexity barriers arising from quantum compression, while making no broad claims about typical cases or the performance and trainability of algorithm pipelines that use it.