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arXiv:1812.08451 · Quantum

Optimizing Quantum Error Correction Codes with Reinforcement Learning

Hendrik Poulsen Nautrup, Nicolas Delfosse, Vedran Dunjko, Hans J. Briegel, Nicolai Friis

Published Dec 16, 2019• 162 citations
arXivHTMLPDF

Abstract

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.

DOI
10.22331/q-2019-12-16-215

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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.
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With a particular emphasis on fixing fault defects caused by bitflip and depolarizing noise, this study explores the use of RL methods within the framework of quantum error correction. This work investigates the flexibility and independence of RL-trained agents in reducing bitflip mistakes by methodically looking at error rates and qubit lifetimes. Furthermore, we study how the top-performing agents are affected by depolarizing noise and present a strategic "Decoded Surface Code" method for fixing mistakes. The results show how RL works in handling different types of errors on its own, revealing subtle dynamics in the quantum system. Quantum error correction is a rapidly developing area, and this study adds to it by shedding light on how reinforcement learning could improve quantum computing's fault tolerance. The study's findings provide a basis for future research into more robust quantum computing systems and have ramifications for the creation of autonomous error-correcting algorithms.
Quantum error correction (QEC) is a crucial element in the realization of fault-tolerant quantum computation. However, traditional QEC schemes often rely on pre-determined, static parameters, which may not be optimally suited for the specific noise characteristics present in a given quantum hardware. This work introduces a novel approach to QEC that leverages reinforcement learning (RL) to dynamically adapt the error correction protocol in real-time. The system learns to optimize the parameters of the QEC code, such as measurement schedules and decoding strategies, based on continuous feedback from the quantum hardware. This adaptive approach promises to significantly improve the performance and efficiency of QEC, reducing the overhead associated with error correction and enhancing the fidelity of quantum computations. The core claim of this paper is that quantum error correction is computationally intensive and requires precise control over quantum systems. The central mechanism involves employing reinforcement learning to optimize the parameters of quantum error correction protocols in real-time, adapting to the specific noise characteristics of the quantum hardware. This represents a new automation of the QEC process.
Abstract In the ongoing race towards experimental implementations of quantum error correction (QEC), finding ways to automatically discover codes and encoding strategies tailored to the qubit hardware platform is emerging as a critical problem. Reinforcement learning (RL) has been identified as a promising approach, but so far it has been severely restricted in terms of scalability. In this work, we significantly expand the power of RL approaches to QEC code discovery. Explicitly, we train an RL agent that automatically discovers both QEC codes and their encoding circuits for a given gate set, qubit connectivity and error model, from scratch. This is enabled by a reward based on the Knill-Laflamme conditions and a vectorized Clifford simulator, showing its effectiveness with up to 25 physical qubits and distance 5 codes, while presenting a roadmap to scale this approach to 100 qubits and distance 10 codes in the near future. We also introduce the concept of a noise-aware meta-agent, which learns to produce encoding strategies simultaneously for a range of noise models, thus leveraging transfer of insights between different situations. Our approach opens the door towards hardware-adapted accelerated discovery of QEC approaches across the full spectrum of quantum hardware platforms of interest.
The design and optimization of quantum codes is generally hard because of the prohibitive computational cost. The recently introduced quantum lego framework provides a powerful method for generating complex quantum error-correcting codes (QECCs) out of simple ones. We gamify this process and unlock a new avenue for code design and discovery using reinforcement learning (RL). Already for simple code measures and modest qubit numbers, we produce codes that are both optimal and novel. Moreover, we argue that this framework is both scalable, when combined with efficient tensor contraction methods, and flexible, since we can specify arbitrary properties of the code to be optimized. We train on two such properties, maximizing the code distance, and minimizing the probability of logical error under biased Pauli noise. For the first, we show that the trained agent identifies ways to increase code distance beyond naive concatenation, saturating the linear programming bound for CSS (Calderbank, Shor, Steane) codes on 13 qubits. With a learning objective to minimize the logical error probability under biased Pauli noise, we find the best-known CSS code at this task for $\ensuremath{\lesssim}20$ qubits. Compared to other (locally deformed) CSS codes, including Surface, XZZX, and two-dimensional Color codes, our [[17,1,3]][[17,1,3]][[17,1,3]] code construction actually has lower adversarial distance, yet better protects the logical information, highlighting the importance of QECC desiderata. Lastly, we comment on how this RL framework can be used in conjunction with physical quantum devices to tailor a code without explicit characterization of the noise model.