Abstract
The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work we implement cutting-edge Reinforcement Learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in non-integrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum state manipulation, viewed as an optimization problem, exhibits a spin-glass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics.
Highlights
Reliable quantum-state manipulation is essential for many areas of physics ranging from nuclear-magneticresonance experiments [1] and cold atomic systems [2,3] to trapped ions [4,5,6], quantum optics [7], superconducting qubits [8], nitrogen-vacancy centers [9], and quantum computing [10]
machine learning (ML) has recently been applied successfully to several problems in equilibrium condensed matter physics [46,47], turbulent dynamics [48,49], and experimental design [50,51], and here we demonstrate that reinforcement learning (RL) provides deep insights into nonequilibrium quantum dynamics [52,53,54,55,56,57]
The learning process is shown in Video 7 of Supplemental Material [62]. (ii) We reveal an important novel perspective on the complexity of quantum-state manipulation which, as we show below, generalizes to many-particle systems
Summary
Reliable quantum-state manipulation is essential for many areas of physics ranging from nuclear-magneticresonance experiments [1] and cold atomic systems [2,3] to trapped ions [4,5,6], quantum optics [7], superconducting qubits [8], nitrogen-vacancy centers [9], and quantum computing [10]. The quantum speed limit [63], exploration becomes vital and offers an alternative to the prevalent paradigm of multistarting local gradient optimizers [64] Unlike these methods, the RL agent progressively learns to build a model of the optimization landscape in such a way that the protocols it finds are stable to sampling noise. The RL agent progressively learns to build a model of the optimization landscape in such a way that the protocols it finds are stable to sampling noise In this regard, RL-based approaches may be well suited to work with experimental data and do not require explicit knowledge of local gradients of the control landscape [59,62]. An additional advantage of focusing on bang-bang protocols is that this allows us to interpret the control phase transitions we find using the language of statistical mechanics [67]
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