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arXiv:2504.10938 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Iterative Linear Quadratic Regulator for Quantum Optimal Control

Dirk Heimann, Felix Wiebe, Tahereh Abad, Elie Mounzer, Tangyou Huang, Frank Kirchner, Shivesh Kumar

Published Aug 30, 2025• 0 citations
arXivHTMLPDF

Abstract

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$\mathbf{X}$and cross-resonance gates on one- and two-qubit fixed-frequency transmons simulated with two and three levels.

DOI
10.1109/qce65121.2025.00152

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Abstract Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant amount of (classical) computation required to generate customized gates can quickly undermine the effectiveness of this approach, especially when pulse optimization needs to be iterated. We propose a method to reduce the computational time required to generate the control pulse for a Hamiltonian that is parametrically dependent on a time-varying quantity. We use simple interpolation schemes to accurately reconstruct the control pulses from a set of pulses obtained in advance for a discrete set of predetermined parameter values. We obtain a reconstruction with very high fidelity and a significant reduction in computational effort. We report the results of the application of the proposed method to device-level quantum simulations of the unitary (real) time evolution of two interacting neutrons based on superconducting qubits.
We present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs a sequence of unconstrained numerical optimal control cycles that each minimize the gate fidelity for a given gate duration alongside an additional penalty term for the control pulse amplitudes. After each cycle, the gate duration is adjusted based on the inverse of the resulting maximum control pulse amplitudes by re-scaling the dynamics to a new duration where control pulses satisfy the amplitude constraints. Those scaled controls then serve as an initial guess for the next unconstrained optimal control cycle, using the adjusted gate duration. We provide multiple numerical examples that each demonstrate fast convergence of the scheme toward a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound. The proposed technique is agnostic to the underlying system and control Hamiltonian models, as well as the target unitary gate operation, making the time-scaling iteration an easy to implement and practically useful scheme for reducing the durations of quantum gate operations.
Abstract The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.