arXiv subjects

Dirk Heimann

Publications and source records attributed to Dirk Heimann.

4 recordsLinked to original sources

arXiv2026

Iterative linear quadratic regulator on SU(N) for multi-qubit gate synthesis

In quantum optimal control theory, gradient-based trajectory optimization techniques have proven versatile in designing multi-qubit quantum gates. Furthermore, incorporating the underlying Lie-group structure can accelerate the optimization process. In this work, we adapt the Lie-group formulation of the iterative linear quadratic regulator (iLQR) to the special unitary group SU(N) and apply it to quantum gate synthesis, systematically comparing it against the standard Euclidean iLQR formulation across multiple two- to five-qubit gates. We find that in the idealized, unconstrained setting, where all Lie-algebra basis elements are available as drive Hamiltonian terms, the Lie-group formulation converges faster than the Euclidean iLQR formulation. If drive terms are constrained to 2-local Hamiltonian terms, the Lie-group variant converges faster in early optimization iterations, but exhibits greater sensitivity to initialization and a stronger tendency towards local minima. These results demonstrate that incorporating Lie-group geometry into iLQR substantially improves convergence and highlight important next steps for improvements in constrained control settings.

quant-ph↗

arXiv2025

Learning Fourier series with parametrized quantum circuits

Variational quantum algorithms (VQAs) and their applications in the field of quantum machine learning through parametrized quantum circuits (PQCs) are thought to be one major way of leveraging noisy intermediate-scale quantum computing devices. However, differences in the performance of certain VQA architectures are often unclear since established best practices, as well as detailed studies, are missing. In this paper, we build upon the work by Schuld et al. [Phys. Rev. A 103, 032430 (2021)] and Vidal et al. [Front. Phys. 8, 297 (2020)] by comparing how well popular ansätze for PQCs learn different one-dimensional truncated Fourier series. We also examine dissipative quantum neural networks (dQNN) as introduced by Beer et al. [Nat. Commun. 11, 808 (2020)] and propose a data reupload structure for dQNNs to increase their capability for this regression task. By comparing the results for different PQC architectures, we can provide guidelines for designing efficient PQCs.

quant-ph↗

arXiv2025

Iterative Linear Quadratic Regulator for Quantum Optimal Control

Quantum optimal control for gate optimization aims to provide accurate, robust, and fast pulse sequences to achieve gate fidelities on quantum systems below the error correction threshold. Many methods have been developed and successfully applied in simulation and on quantum hardware. In this paper, we establish a connection between the iterative linear quadratic regulator and quantum optimal control by adapting it to gate optimization of quantum systems. We include constraints on the controls and their derivatives to enable smoother pulses. We achieve high-fidelity simulation results for X and cross-resonance gates on one- and two-qubit fixed-frequency transmons simulated with two and three levels.

quant-ph↗

arXiv2024

Quantum Deep Reinforcement Learning for Robot Navigation Tasks

We utilize hybrid quantum deep reinforcement learning to learn navigation tasks for a simple, wheeled robot in simulated environments of increasing complexity. For this, we train parameterized quantum circuits (PQCs) with two different encoding strategies in a hybrid quantum-classical setup as well as a classical neural network baseline with the double deep Q network (DDQN) reinforcement learning algorithm. Quantum deep reinforcement learning (QDRL) has previously been studied in several relatively simple benchmark environments, mainly from the OpenAI gym suite. However, scaling behavior and applicability of QDRL to more demanding tasks closer to real-world problems e. g., from the robotics domain, have not been studied previously. Here, we show that quantum circuits in hybrid quantum-classic reinforcement learning setups are capable of learning optimal policies in multiple robotic navigation scenarios with notably fewer trainable parameters compared to a classical baseline. Across a large number of experimental configurations, we find that the employed quantum circuits outperform the classical neural network baselines when equating for the number of trainable parameters. Yet, the classical neural network consistently showed better results concerning training times and stability, with at least one order of magnitude of trainable parameters more than the best-performing quantum circuits. However, validating the robustness of the learning methods in a large and dynamic environment, we find that the classical baseline produces more stable and better performing policies overall.

cs.RO↗