Kappen group
Radboud University, Nijmegen, Netherlands
- Website
- www.ru.nl/en/people/kappen-h
- Tracked papers
- 2 (2024–2025)
Topics
The most frequent field-map topics among the PI' tracked papers.
Recent papers
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Path Integral Quantum Control for Quantum Chemistry Applications
Abstract
The Path integral Quantum Control (PiQC) algorithm was recently introduced by Villanueva et al. (2025) as a new approach for computing optimal controls in open and closed quantum systems. Originally proposed for pulse-based quantum control, PiQC estimates optimal controls through global averages over quantum trajectories. In this work, we adapt the PiQC algorithm to optimize parametrized quantum circuits by showing that the quantum circuit can be randomized using a continuous dynamics governed by a stochastic Schrödinger equation that is compatible with the path integral control framework. In this adaptation, the circuit parameters become the controls to be optimized within PiQC. We refer to this instance of PiQC as the Gate-based PiQC (GB-PiQC) algorithm. We apply GB-PiQC for ground state preparation of electronic structure problems. We benchmark the gate-based and pulse-based versions of PiQC against the Variational Quantum Eigensolver (VQE), which is optimized using the common Simultaneous Perturbation Stochastic Approximation (SPSA) optimizer, on a set of standard molecular Hamiltonians: H2, LiH, BeH2, and H4, mapped to 2-, 4-, 6-, and 6-qubit systems, respectively. For each molecule, the benchmark is implemented at different bond distances, after performing a hyperparameter tuning of each algorithm at a fixed bond distance near the equilibrium geometry. We find that both PiQC algorithms exhibit greater robustness than SPSA to variations in the target Hamiltonian induced by changes in molecular bond distances. Furthermore, PiQC algorithms also achieve superior performance compared to SPSA in most instances, particularly at stretched bond lengths, where the Hartree-Fock solution becomes less accurate and its error grows relative to equilibrium.
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Path integral control of open quantum systems
Abstract
We investigate open-loop quantum state preparation for a class of open quantum systems whose dynamics follow a Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation that admits a trajectory-based stochastic representation. The deterministic control objective is reformulated as a stochastic optimal control problem -- interpreting stochasticity as a methodological tool akin to stochastic Schrödinger equation unravelings -- which situates the problem within the path integral control framework. For the class of GKLS generators under consideration, this reformulation leads to an explicit expression for the optimal control as a weighted average over stochastic quantum trajectories, thereby eliminating the need for gradient evaluations. Building on this theoretical result, we derive a control update rule for piecewise-constant control pulses and demonstrate that adaptive importance sampling progressively enhances the control estimator during optimization, culminating in the algorithm we term Path integral Quantum Control (PiQC). We further introduce an annealed variant of PiQC, wherein a synthetic noise schedule gradually steers open-system trajectories toward closed-system dynamics, enabling high-fidelity unitary state preparation. Numerical studies on a dissipative single-qubit system and a multi-qubit Nuclear Magnetic Resonance model verify that PiQC yields precise open-loop controls and displays robustness to Hamiltonian perturbations. We propose PiQC as a trajectory-based alternative to gradient-based approaches, which might offer a viable solution in quantum control problems where gradient computation is infeasible or computationally demanding.