arXiv subjects

Michael Poppel

Publications and source records attributed to Michael Poppel.

8 recordsLinked to original sources

arXiv2026

Exploiting Symmetry in Quantum Reservoir Computing

Quantum reservoir computing (QRC) uses a quantum processor without training it. The input is encoded into a quantum state, a fixed random circuit evolves it, selected observables are measured, and only a simple linear readout is trained on the measured values. We study QRC for forecasting on a ring of sensors, such as weather stations around a circle of latitude. On such a ring, the same physical rule governs every position, so a model that respects this symmetry can learn one shared local rule from all sensors at once instead of a separate rule per sensor. This is especially valuable when data is scarce. Because the readout sees only the measured numbers, the symmetry can be lost even when the quantum state respects it. We show how to preserve the symmetry by measuring every observable together with all its shifted copies and by using one shared rule for encoding, circuit, and readout, and we prove that this construction is sufficient. In a controlled audit the aligned design consistently outperforms misaligned alternatives, and the advantage persists in noisy simulations, on IBM hardware, and on real weather data.

quant-ph↗

arXiv2026

Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency

Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical frequency redundancy, and require the same minimum parameter count for coefficient control. Despite this equivalence, trainability varies substantially with architecture shape $(N,L)$ at fixed $E$. We identify structural rank deficiency of the coefficient matching Jacobian $J$ as the mechanism responsible. For serial single-qubit architectures, we prove $\mathrm{rank}(J) \leq 2L+1$ regardless of parameter count $P$, with $\dim(\ker J) \geq P-(2L+1)$ growing without bound -- a phenomenon we term \emph{structural gradient starvation}: a growing fraction of parameters become structurally decoupled from the loss as $P$ increases at fixed $L$. Parallel architectures avoid this via independent phase trajectories, ensuring $\sigma_{\min}(J^{(\mathrm{par})}) > 0$ generically for $P \leq 2E+1$, so no parameter lies in $\ker J$. For practitioners, we further show that the two natural routes to increasing parameter count have fundamentally different effects: adding feature map (FM) layers monotonically strengthens the Jacobian QFIM eigenvalue spectrum and achieves $R^2 \geq 0.95$ with $1.6$--$2.2\times$ fewer parameters than adding trainable blocks across all tested architectures, while trainable blocks improve training only through the classical interpolation mechanism with no quantum-specific benefit.

quant-ph↗

arXiv2026

Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers

The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state evolution to a feasible subspace, such as the Hamming-weight-1 sector for one-hot constraints. On the contrary, warm-starting biases the search toward promising regions based on preliminary solutions. Combining these two techniques requires maintaining the essential alignment between the initial state and the mixer Hamiltonian to preserve convergence guarantees. Previous work demonstrated warm-starting with XY-mixers via a biased initial state, but relying only on standard mixer Hamiltonians. Consequently, the initial state is no longer a ground state of the mixer. In this work, we overcome these limitations by formulating a warm-started XY-mixer Hamiltonian for one-hot constraints and proving its ground-state properties. Furthermore, we provide a shallow circuit implementation suitable for NISQ implementations. We embed the warm-starting into a classical heuristic that iteratively updates the bias based on previous samples, called Iterative Warm-Starting (IWS). Extensive numerical simulations on Max-$k$-Cut and Traveling Salesperson Problem instances demonstrate that IWS-QAOA significantly accelerates the solution-finding process, increasing the probability of sampling optimal solutions by orders of magnitude compared to standard XY-QAOA. Finally, we validate our approach on the ibm_boston QPU using hardware-tailored 144-qubit problem instances. By coupling IWS-QAOA with a greedy steepest-descent post-processing strategy to repair infeasible measurements caused by hardware noise, we successfully identify optimal solutions on actual quantum devices.

quant-ph↗

arXiv2026

Long Range Frequency Tuning for QML

Angle-encoded variational quantum circuits admit a truncated Fourier series representation of their output, but approximating functions with maximum frequency $\omega_{\max}$ using fixed unary encoding requires $\mathcal{O}(\omega_{\max})$ encoding gates. Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose \emph{ternary grid initialization} -- setting prefactors to $\{1, 3, 9, \ldots, 3^{k-1}\}$ -- which ensures every target frequency within $[-\omega_{\max}, \omega_{\max}]$ lies within $\tfrac{1}{2}$ unit of the accessible spectrum at initialization, so that the spectral-gap bound no longer constrains the target-driven gradient to be small. This is a necessary condition for reliable convergence, whose sufficiency we establish empirically. On a synthetic benchmark with target frequencies shifted well beyond the standard initialization range, ternary initialization achieves median $R^2 = 0.997$ versus $0.18$ for unary initialization, with $100\%$ of runs achieving $R^2 > 0.95$ against $0\%$. CMA-ES with $20\times$ the evaluation budget reaches only $25\%$ success, confirming the limitation is a property of the optimization landscape rather than of gradient-based optimization specifically. Real-world validation on two benchmark datasets demonstrates consistent advantages over both fixed and trainable unary baselines.

cs.LG↗

arXiv2025

Topology-Guided Quantum GANs for Constrained Graph Generation

Quantum computing (QC) promises theoretical advantages, benefiting computational problems that would not be efficiently classically simulatable. However, much of this theoretical speedup depends on the quantum circuit design solving the problem. We argue that QC literature has yet to explore more domain specific ansatz-topologies, instead of relying on generic, one-size-fits-all architectures. In this work, we show that incorporating task-specific inductive biases -- specifically geometric priors -- into quantum circuit design can enhance the performance of hybrid Quantum Generative Adversarial Networks (QuGANs) on the task of generating geometrically constrained K4 graphs. We evaluate a portfolio of entanglement topologies and loss-function designs to assess their impact on both statistical fidelity and compliance with geometric constraints, including the Triangle and Ptolemaic inequalities. Our results show that aligning circuit topology with the underlying problem structure yields substantial benefits: the Triangle-topology QuGAN achieves the highest geometric validity among quantum models and matches the performance of classical Generative Adversarial Networks (GAN). Additionally, we showcase how specific architectural choices, such as entangling gate types, variance regularization and output-scaling govern the trade-off between geometric consistency and distributional accuracy, thus emphasizing the value of structured, task-aware quantum ansatz-topologies.

quant-ph↗

arXiv2025

Mitigating Exponential Mixed Frequency Growth through Frequency Selection

Angle encoding has emerged as a popular feature map for embedding classical data into quantum models, naturally generating truncated Fourier series with universal function approximation capabilities. Despite this expressive capability, practical training faces significant challenges. Through controlled experiments with white-box target functions, we demonstrate that training failures can occur even when all established parameter sufficiency conditions are satisfied. Building on the redundancy-gradient framework of Duffy and Jastrzebski, we provide systematic experimental evidence that non-unique frequencies dominate the gradient landscape and crowd out target frequencies -- a burden that grows exponentially with encoding depth under unary encoding. Small-angle initialization mitigates this in one-dimensional settings but fails to scale to higher dimensions, where even ternary encoding -- which minimizes per-frequency redundancy -- faces intractable combinatorial growth of unique frequency tuples regardless of initialization or optimizer choice. We introduce frequency selection as a principled solution that restricts the model spectrum to only those frequencies present in the target function. For two-dimensional targets, frequency selection achieves near-optimal performance (median $R^2 \approx 0.95$) where dense approaches struggle, and remains tractable at high-frequency magnitudes where dense approaches fail entirely (median $R^2 \approx 0.85$). Validation on a real-world dataset confirms the approach transfers beyond synthetic settings.

quant-ph↗

arXiv2025

Solving a real-world modular logistic scheduling problem with a quantum-classical metaheuristics

This study evaluates the performance of a quantum-classical metaheuristic and a traditional classical mathematical programming solver, applied to two mathematical optimization models for an industry-relevant scheduling problem with autonomous guided vehicles (AGVs). The two models are: (1) a time-indexed mixed-integer linear program, and (2) a novel binary optimization problem with linear and quadratic constraints and a linear objective. Our experiments indicate that optimization methods are very susceptible to modeling techniques and different solvers require dedicated methods. We show in this work that quantum-classical metaheuristics can benefit from a new way of modeling mathematical optimization problems. Additionally, we present a detailed performance comparison of the two solution methods for each optimization model.

quant-ph↗

arXiv2023

Benchmarking Quantum Surrogate Models on Scarce and Noisy Data

Surrogate models are ubiquitously used in industry and academia to efficiently approximate given black box functions. As state-of-the-art methods from classical machine learning frequently struggle to solve this problem accurately for the often scarce and noisy data sets in practical applications, investigating novel approaches is of great interest. Motivated by recent theoretical results indicating that quantum neural networks (QNNs) have the potential to outperform their classical analogs in the presence of scarce and noisy data, we benchmark their qualitative performance for this scenario empirically. Our contribution displays the first application-centered approach of using QNNs as surrogate models on higher dimensional, real world data. When compared to a classical artificial neural network with a similar number of parameters, our QNN demonstrates significantly better results for noisy and scarce data, and thus motivates future work to explore this potential quantum advantage in surrogate modelling. Finally, we demonstrate the performance of current NISQ hardware experimentally and estimate the gate fidelities necessary to replicate our simulation results.

quant-ph↗