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arXiv:2502.02198 · The Journal of Chemical Physics

Instrumental distortions in quantum optimal control

Uluk Rasulov, Ilya Kuprov

Published Apr 25, 2025• 8 citations
arXivHTMLPDF

Abstract

Quantum optimal control methods, such as gradient ascent pulse engineering (GRAPE), are used for precise manipulation of quantum states. Many of those methods were pioneered in magnetic resonance spectroscopy, where instrumental distortions are often negligible. However, that is not the case elsewhere: the usual jumble of cables, resonators, modulators, splitters, amplifiers, and filters can and would distort control signals. Those distortions may be non-linear; their inverse functions may be ill-defined and unstable; they may even vary from one day to the next and across the sample. Here we introduce the response-aware gradient ascent pulse engineering framework, which accounts for any cascade of differentiable distortions within the GRAPE optimization loop, does not require filter function inversion, and produces control sequences that are resilient to user-specified distortion cascades with user-specified parameter ensembles. The framework is implemented into the optimal control module supplied with versions 2.10 and later of the open-source Spinach library; the user needs to provide function handles returning the actions by the distortions and, optionally, parameter ensembles for those actions.

DOI
10.1063/5.0264092

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Quantum optimal control methods, such as gradient ascent pulse engineering (GRAPE), are used for precise manipulation of quantum states. Many of those methods were pioneered in magnetic resonance spectroscopy, where instrumental distortions are often negligible. However, that is not the case elsewhere: the usual jumble of cables, resonators, modulators, splitters, amplifiers, and filters can and would distort control signals. Those distortions may be non-linear; their inverse functions may be ill-defined and unstable; they may even vary from one day to the next and across the sample. Here we introduce the response-aware gradient ascent pulse engineering framework, which accounts for any cascade of differentiable distortions within the GRAPE optimization loop, does not require filter function inversion, and produces control sequences that are resilient to user-specified distortion cascades with user-specified parameter ensembles. The framework is implemented into the optimal control module supplied with versions 2.10 and later of the open-source Spinach library; the user needs to provide function handles returning the actions by the distortions and, optionally, parameter ensembles for those actions.
Quantum optimal control, a powerful toolbox for engineering an optimal control field modulation that most precisely implements a desired quantum operation in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The gradient ascent pulse engineering (GRAPE) algorithm is a widely used method in quantum optimal control, which has achieved great success in different physical platforms. However, its computational complexity increases exponentially with the number of qubits, making it challenging to be implemented for large-scale quantum systems. To mitigate this issue, we present the iterative GRAPE algorithm (iGRAPE), which reduces the optimization problem into a series of lower-dimensional subproblems by incorporating disentanglement operations. Our numerical simulations on physical platforms such as nuclear magnetic resonance and superconducting quantum systems demonstrate that iGRAPE significantly enhances state preparation speed. Specifically, compared to GRAPE, iGRAPE achieves up to a five-fold acceleration in preparing Greenberger--Horne--Zeilinger states using a 12-qubit implementation, and up to a 13-fold acceleration for arbitrary state preparation with eight qubits. To further validate our findings, we conduct experimental validation of iGRAPE on a four-qubit nuclear magnetic resonance system. Overall, iGRAPE offers an efficient solution for implementing optimal control in large-scale quantum systems, holding great potential for advancing quantum technologies during the noisy intermediate-scale quantum era.
The GRAPE...jl package (https://github.com/JuliaQuantumControl/GRAPE.jl) implements Gradient Ascent Pulse Engineering, a widely used method of quantum optimal control. Its purpose is to find controls that steer a quantum system in a particular way. This is a prerequisite for next-generation quantum technology, such as quantum computing or quantum sensing. GRAPE...jl exploits the unique strengths of the Julia programming language to achieve both flexibility and numerical performance. It builds on the QuantumControl...jl framework.
Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.
We present an iterative optimal control method of quantum systems, aimed at an implementation of a desired operation with optimal fidelity. The update step of the method is based on the linear response of the fidelity to the control operators, and its projection onto the mode functions of the corresponding operator. Our method extends methods such as gradient-ascent pulse engineering (GRAPE) and variational quantum algorithms, by determining the fidelity gradient in a hyperparameter-free manner, and using it for a multiparameter update, capitalizing on the multimode overlap of the perturbation and the mode functions. This directly reduces the number of dynamical trajectories that need to be evaluated in order to update a set of parameters. We demonstrate this approach, and compare it to the standard GRAPE algorithm, for the example of a quantum gate on two qubits, demonstrating a clear improvement in convergence and optimal fidelity of the generated protocol.
Control and simulation of spin dynamics face two persistent bottlenecks: instrument-induced distortions that warp optimised pulses, and the near universal piecewise-constant approximation of the Hamiltonian. The latter is the lowest order Lie-solver that degrades under fast timing and realistic hardware responses. This thesis addresses both. From first principles, piecewise-linear and piecewise-quadratic propagators that evolve on the Lie-group manifold are derived. In simulation, these higher-order Lie-solvers achieve higher trajectory accuracy with fewer time intervals. The GRadient Ascent Pulse Engineering (GRAPE) algorithm is extended to a piecewise-linear formulation (LGRAPE). The exact analytical gradients are computed via auxiliary matrix methods, delivering higher fidelities under tight timing constraints. When significant, distortions are treated explicitly by embedding cascades of transfer functions and ensemble parameters directly into the optimisation. The resulting Response-Aware GRAPE (RAW-GRAPE) requires only the transfer functions and their Jacobians (via automatic differentiation when needed), compensating for linear/non-linear effects without brittle deconvolution. Single-pole and single-zero blocks are supplied that act as basis elements for arbitrary linear responses. When combined with non-linear elements, the framework can, in principle, incorporate any distortion cascade. Across diverse simulated experiments with representative hardware artefacts, RAW-GRAPE demonstrates higher robustness and target fidelity compared to conventional GRAPE. As machine learning use expands, well-labelled experimental datasets remain scarce. We therefore build a forward-modelled simulation pipeline that mirrors real experiments and injects hardware artefacts on the fly. The 3D data volume bottleneck is addressed by retaining Kronecker factorisations, avoiding explicit tensor expansion. Hundreds of thousands of spectra are generated in hours to train neural networks for automated protein-backbone assignment. The pipeline integrates with CcpNmr and yields accurate end-to-end predictions on proteins up to 40 kDa. All methods are implemented in Spinach with reproducible workflows.
Efficient approaches to quantum control and feedback are essential for quantum technologies, from sensing to quantum computation.Open-loop control tasks have been successfully solved using optimization techniques, including methods such as gradient-ascent pulse engineering (GRAPE) , relying on a differentiable model of the quantum dynamics.For feedback tasks, such methods are not directly applicable, since the aim is to discover strategies conditioned on measurement outcomes.In this work, we introduce feedback GRAPE, which borrows some concepts from model-free reinforcement learning to incorporate the response to strong stochastic (discrete or continuous) measurements, while still performing direct gradient ascent through the quantum dynamics.We illustrate its power considering various scenarios based on cavity-QED setups.Our method yields interpretable feedback strategies for state preparation and stabilization in the presence of noise.Our approach could be employed for discovering strategies in a wide range of feedback tasks, from calibration of multiqubit devices to linear-optics quantum computation strategies, quantum enhanced sensing with adaptive measurements, and quantum error correction.