Quantum Optimal Control via Semi-Automatic Differentiation

Michael H. Goerz, Sebastián C. Carrasco, and Vladimir S. Malinovsky

DEVCOM Army Research Laboratory, 2800 Powder Mill Road, Adelphi, MD 20783, USA

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We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages, $\tt{GRAPE.jl}$ and $\tt{Krotov.jl}$, part of the $\tt{QuantumControl.jl}$ framework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.

In quantum optimal control theory, we seek to find control fields, e.g., the amplitude of a microwave pulse in a superconducting circuit, to steer a quantum system in some way, e.g., to implement an entangling gate for a quantum computer. A standard method is to iteratively improve the control field based on the gradient of the error with respect to the amplitudes of the control field at each point in time, based on a numerical simulation of the quantum dynamics. In recent years, automatic differentiation (AD) has been adapted from machine learning to quantum control to easily obtain the gradients for arbitrary, even non-analytical optimization functionals. However, AD has an exorbitant numerical overhead, which prevents it from scaling to problems of larger size. Here, we develop the concept of "semi-automatic differentiation" (semi-AD) that eliminates this overhead and can optimize for arbitrary functionals with the same numerical cost as the traditional GRAPE method. We have implemented semi-AD in the Julia programming language in the GRAPE.jl and Krotov.jl packages, part of the QuantumControl.jl framework, and use this implementation to benchmark against both a full-AD optimization and traditional GRAPE. We also demonstrate the power of the approach by directly optimizing the non-analytical entangling power of a quantum gate for the first time.

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Cited by

[1] Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim A. Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini, Lei Wang, Sebastian J. Wetzel, Giuseppe Carleo, Eliška Greplová, Roman Krems, Florian Marquardt, Michał Tomza, Maciej Lewenstein, and Alexandre Dauphin, "Modern applications of machine learning in quantum sciences", arXiv:2204.04198, (2022).

[2] Jonathan A. Jones, "Controlling NMR spin systems for quantum computation", arXiv:2402.01308, (2024).

[3] Georg Raithel, Alisher Duspayev, Bineet Dash, Sebastián C. Carrasco, Michael H. Goerz, Vladan Vuletić, and Vladimir S. Malinovsky, "Principles of tractor atom interferometry", Quantum Science and Technology 8 1, 014001 (2023).

[4] E. Dionis and D. Sugny, "Time-optimal control of two-level quantum systems by piecewise constant pulses", Physical Review A 107 3, 032613 (2023).

[5] Yunwei Lu, Sandeep Joshi, Vinh San Dinh, and Jens Koch, "Optimal control of large quantum systems: assessing memory and runtime performance of GRAPE", Journal of Physics Communications 8 2, 025002 (2024).

[6] Irtaza Khalid, Carrie A. Weidner, Edmond A. Jonckheere, Sophie G. Schirmer, and Frank C. Langbein, "Sample-efficient model-based reinforcement learning for quantum control", Physical Review Research 5 4, 043002 (2023).

[7] V. N. Petruhanov and A. N. Pechen, "GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls", Journal of Physics A Mathematical General 56 30, 305303 (2023).

[8] Alberto Castro, "qocttools: A program for quantum optimal control calculations", Computer Physics Communications 295, 108983 (2024).

[9] Kemal Bidzhiev, Aleksander Wennersteen, Mourad Beji, Mario Dagrada, Mauro D'Arcangelo, Sebastian Grijalva, Anne-Claire Le Henaff, Anton Quelle, and Alvin Sashala Naik, "Cloud on-demand emulation of quantum dynamics with tensor networks", arXiv:2302.05253, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-03-02 16:26:02). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2024-03-02 16:26:01: Encountered the unhandled forward link type postedcontent_cite while looking for citations to DOI 10.22331/q-2022-12-07-871.