Optimizing Quantum Error Correction Codes with Reinforcement Learning

Hendrik Poulsen Nautrup1, Nicolas Delfosse2, Vedran Dunjko3, Hans J. Briegel1,4, and Nicolai Friis5,1

1Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria
2Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA
3LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
4Department of Philosophy, University of Konstanz, Konstanz 78457, Germany
5Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria

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Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a reinforcement learning framework for optimizing and fault-tolerantly adapting quantum error correction codes. We consider a reinforcement learning agent tasked with modifying a family of surface code quantum memories until a desired logical error rate is reached. Using efficient simulations with about 70 data qubits with arbitrary connectivity, we demonstrate that such a reinforcement learning agent can determine near-optimal solutions, in terms of the number of data qubits, for various error models of interest. Moreover, we show that agents trained on one setting are able to successfully transfer their experience to different settings. This ability for transfer learning showcases the inherent strengths of reinforcement learning and the applicability of our approach for optimization from off-line simulations to on-line laboratory settings.

Many promising quantum technologies, ranging from powerful quantum computers to ultra-sensitive measuring devices, are currently being developed and tested in small-scale experiments around the globe. These devices are all strongly affected by noise from their environment and have to be controlled very precisely. This can be done via a technique called quantum error correction. However, this typically requires significant additional resources which are scarce and expensive. It is therefore crucial to find effective error correction procedures that use as few resources as possible. Unfortunately, this is very difficult in many cases. This work presents a flexible and efficient method based on artificial intelligence techniques for determining the best error correction strategy given available resources.

We develop an approach to quantum error correction where a machine learning algorithm (or learning agent) learns to design good error correction tools (called codes) that use as few basic building elements (qubits) as possible. We provide extensive computer simulations of this method for various realistic situations with qubit numbers soon available in state-of-the art laboratories. Our results suggest that a learning agent can not only find near-optimal solutions for a variety of problems, but is also able to transfer its experience from one situation to another. This feature is particularly valuable because it facilitates pre-training learning agents on cheap simulations before deployment to the actual, expensive device. Our work thus provides a stepping-stone for connecting quantum technologies and artificial intelligence that can be vital for future quantum devices.

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