arXiv subjects

Melvin Strobl

Publications and source records attributed to Melvin Strobl.

7 recordsLinked to original sources

arXiv2026

Trainable Quantum Spectral Models for Partial Differential Equations

This work studies trainable quantum spectral models (QSMs) for solving linear partial differential equations (PDEs). Instead of learning solutions directly in physical space, QSMs learn the inverse differential operator in a spectral representation, embedding prior knowledge of the equation's natural basis. We systematically study the expressibility and trainability of several QSM architectures, ranging from near-diagonal to fully parameterized unitaries. In particular, we introduce a family of richer spectral models that interpolate between purely diagonal operators and fully mixing unitaries through a parameterized mixer controlled by $\epsilon$. Our results reveal an intermediate regime, typically around $\epsilon \approx 0.5$, where models achieve the best tradeoff between expressibility and trainability. Beyond this threshold, increased circuit complexity degrades convergence without improving accuracy. Among the architectures considered, models inspired by the inverse step of the Harrow-Hassidim-Lloyd (HHL) algorithm achieve the fastest training convergence while maintaining high solution fidelity. Numerical experiments on the (variable-coefficient) Poisson and Helmholtz equations show that trainable operations in the spectral basis outperform standard variational quantum circuits acting directly in the computational basis. These advantages appear through faster convergence, more stable gradients, and more accurate recovery of the reference solution spectrum, particularly through stronger suppression of spurious high-frequency components, even when the operator is not exactly diagonal in the chosen spectral basis. Our results identify operator-aware spectral representations as a promising route toward trainable and physically grounded quantum methods for scientific computing.

quant-ph↗

arXiv2026

Software Between Quantum and Machine Learning -- And Down to Pulses

Contemporary quantum computing platforms remain, in essence, programmable physical systems whose control is typically mediated through unitary gate abstractions. While such abstractions provide a uniform interface, they obscure important aspects of the underlying hardware and may limit the exploitation of its full capabilities. Direct operation at the control-pulse level offers a more expressive and physically faithful paradigm, enabling, for instance, the implementation of tailored error-mitigation and optimisation strategies. However, this increased expressivity comes at the cost of greater quantum software development complexity, necessitating structured and accessible tooling. We present a software framework, integrated within the QML-Essentials package, that extends quantum machine learning (QML) methodologies to encompass pulse-level modelling. By embedding quantum optimal control techniques within a QML setting, our approach enables the seamless combination of gate-based and pulse-level representations. The framework provides a comprehensive suite of modelling and analytical capabilities. In particular, we introduce composable ansatz constructions based on interchangeable building blocks, and support for end-to-end optimisation of pulse parameters. Motivated by the central role of quantum Fourier models, we further incorporate a range of Fourier-analytic diagnostics, complemented by extended measures of entanglement. All performance-critical components are implemented in a high-performance environment using JAX and supported by a dedicated quantum simulator. Taken together, the framework facilitates reproducible and systematic investigations, while bridging the conceptual and practical divide between abstract circuit models and hardware-aware optimisation. It provides a robust foundation for future developments at the intersection of QML and quantum control.

quant-ph↗

arXiv2026

Beyond Gates: Pulse Level Quantum Fourier Models

In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and trainability of such models showcasing the potential but also the limitations for the prospective application of QFMs. However, much less is known in the context of pulse-level quantum computing, where the microwave parameters that implement unitary operations on the hardware are used to perform computations directly instead of through the interface of quantum circuits. In this work, we evaluate QFMs through the lens of pulse parameters and link metrics such as expressibility and Fourier coefficient correlation (FCC) to this extended set of variational parameters. We show that while control over pulse shapes does not significantly alter the global expressibility or structural correlations of the Ansatz, it fundamentally alters the local optimisation landscape. For composite gates, independent pulse scalings replace a single logical angle by multiple independently tunable sub-angles. This relaxes the rigid monomial couplings induced by the gate-level parameterisation, and provides gradient descent with higher-dimensional escape routes, decoupling local parameter constraints and significantly boosting performance during training. Following an analytical proof, we show numerical results validating our theory on training a QFM with an exponential (ternary) feature map on a Fourier series with the same frequencies.

quant-ph↗

arXiv2025

Fourier Fingerprints of Ansatzes in Quantum Machine Learning

Typical schemes to encode classical data in variational quantum machine learning (QML) lead to quantum Fourier models with $\mathcal{O}(\exp(n))$ Fourier basis functions in the number of qubits. Despite this, in order for the model to be efficiently trainable, the number of parameters must scale as $\mathcal{O}(\mathrm{poly}(n))$. This imbalance implies the existence of correlations between the Fourier modes, which depend on the structure of the circuit. In this work, we demonstrate that this phenomenon exists and show cases where these correlations can be used to predict ansatz performance. For several popular ansatzes, we numerically compute the Fourier coefficient correlations (FCCs) and construct the Fourier fingerprint, a visual representation of the correlation structure. We subsequently show how, for the problem of learning random Fourier series, the FCC correctly predicts relative performance of ansatzes whilst the widely-used expressibility metric does not. Finally, we demonstrate how our framework applies to the more challenging problem of jet reconstruction in high-energy physics. Overall, our results demonstrate how the Fourier fingerprint is a powerful new tool in the problem of optimal ansatz choice for QML.

quant-ph↗

arXiv2025

Out of Tune: Demystifying Noise-Effects on Quantum Fourier Models

Variational quantum algorithms have received substantial theoretical and empirical attention. As the underlying variational quantum circuit (VQC) can be represented by Fourier series that contain an exponentially large spectrum in the number of input features, hope for quantum advantage remains. Nevertheless, it remains an open problem if and how quantum Fourier models (QFMs) can concretely outperform classical alternatives, as the eventual sources of non-classical computational power (for instance, the role of entanglement) are far from being fully understood. Likewise, hardware noise continues to pose a challenge that will persist also along the path towards fault tolerant quantum computers. In this work, we study VQCs with Fourier lenses, which provides possibilities to improve their understanding, while also illuminating and quantifying constraints and challenges. We seek to elucidate critical characteristics of QFMs under the influence of noise. Specifically, we undertake a systematic investigation into the impact of noise on the Fourier spectrum, expressibility, and entangling capability of QFMs through extensive numerical simulations and link these properties to training performance. The insights may inform more efficient utilisation of quantum hardware and support the design of tailored error mitigation and correction strategies. Decoherence imparts an expected and broad detrimental influence across all Ans\"atze. Nonetheless, we observe that the severity of these deleterious effects varies among different model architectures, suggesting that certain configurations may exhibit enhanced robustness to noise and show computational utility.

quant-ph↗

arXiv2025

QML Essentials -- A framework for working with Quantum Fourier Models

In this work, we propose a framework in the form of a Python package, specifically designed for the analysis of Quantum Machine Learning models. This framework is based on the PennyLane simulator and facilitates the evaluation and training of Variational Quantum Circuits. It provides additional functionality ranging from the ability to add different types of noise to the classical simulation, over different parameter initialisation strategies, to the calculation of expressibility and entanglement for a given model. As an intrinsic property of Quantum Fourier Models, it provides two methods for calculating the corresponding Fourier spectrum: one via the Fast Fourier Transform and another analytical method based on the expansion of the expectation value using trigonometric polynomials. It also provides a set of predefined approaches that allow a fast and straightforward implementation of Quantum Machine Learning models. With this framework, we extend the PennyLane simulator with a set of tools that allow researchers a more convenient start with Quantum Fourier Models and aim to unify the analysis of Variational Quantum Circuits.

quant-ph↗

arXiv2025

From Hope to Heuristic: Realistic Runtime Estimates for Quantum Optimisation in NHEP

Noisy Intermediate-Scale Quantum (NISQ) computers, despite their limitations, present opportunities for near-term quantum advantages in Nuclear and High-Energy Physics (NHEP) when paired with specially designed quantum algorithms and processing units. This study focuses on core algorithms that solve optimisation problems through the quadratic Ising or quadratic unconstrained binary optimisation model, specifically quantum annealing and the Quantum Approximate Optimisation Algorithm (QAOA). In particular, we estimate runtimes and scalability for the task of particle track reconstruction, a key computing challenge in NHEP, and investigate how the classical parameter space in QAOA, along with techniques like a Fourier-analysis based heuristic, can facilitate future quantum advantages. The findings indicate that lower frequency components in the parameter space are crucial for effective annealing schedules, suggesting that heuristics can improve resource efficiency while achieving near-optimal results. Overall, the study highlights the potential of NISQ computers in NHEP and the significance of co-design approaches and heuristic techniques in overcoming challenges in quantum algorithms.

quant-ph↗