Hybrid discrete-continuous compilation of trapped-ion quantum circuits with deep reinforcement learning

Francesco Preti1,2, Michael Schilling1,2, Sofiene Jerbi3,4, Lea M. Trenkwalder3, Hendrik Poulsen Nautrup3, Felix Motzoi1,2, and Hans J. Briegel3

1Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany
2University of Cologne, Institute of Theoretical Physics, , D-50937 Köln, Germany
3University of Innsbruck, Institute for Theoretical Physics, A-6020 Innsbruck, Austria
4Freie Universität Berlin, Dahlem Center for Complex Quantum Systems, D-14195 Berlin, Germany.

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Abstract

Shortening quantum circuits is crucial to reducing the destructive effect of environmental decoherence and enabling useful algorithms. Here, we demonstrate an improvement in such compilation tasks via a combination of using hybrid discrete-continuous optimization across a continuous gate set, and architecture-tailored implementation. The continuous parameters are discovered with a gradient-based optimization algorithm, while in tandem the optimal gate orderings are learned via a deep reinforcement learning algorithm, based on projective simulation. To test this approach, we introduce a framework to simulate collective gates in trapped-ion systems efficiently on a classical device. The algorithm proves able to significantly reduce the size of relevant quantum circuits for trapped-ion computing. Furthermore, we show that our framework can also be applied to an experimental setup whose goal is to reproduce an unknown unitary process.

Whenever we run an algorithm on a classical processor, the abstract programming language that describes our program needs to be compiled in machine language, i.e., instructions that are simple enought to be executed on the logical circuits of the processor. The same is true in quantum computers, where the algorithm, represented by an arbitrary unitary operation, needs to be decomposed in a series of physical operations (laser pulses, microwave pulses, etc.). These simpler unitary operations should be powerful enough together to represent any unitary, in order for the quantum computer to be able to implement any potential quantum algorithm. In this work, we construct a compiler for potentially black-box unitaries based on a bi-level optimization scheme that combines gradient-based optimization for the continuous parameters of the gates and a reinforcement learning scheme for the discrete optimization of the different gate elements. We focus in particular on one of the gate sets usually implemented in trapped-ion quantum computing and develop an anaytic representation of such gate set that allows us not only to calculate analytical gradients with respect to the gate parameters, but also to speeds up our simulations considerably. This enables us to train the reinforcement learning agents for a longer time. We test our method on different compilation tasks that are relevant for trapped-ion computing and observe that it can significantly reduce the size of the circuits required to compile such unitaries.

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[2] Remmy Zen, Jan Olle, Luis Colmenarez, Matteo Puviani, Markus Müller, and Florian Marquardt, "Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning", arXiv:2402.17761, (2024).

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