Deep Reinforcement Learning for Quantum Error Correction - Becker, Marvin; Chiu Falck, Karl-Rehan (My University, 2021)
Recent advancements in quantum computing have supported and reinforced their promising computational abilities which for certain problems far exceeds that of classical computers. However, one of the main difficulties in realising larger quantum computers lies in the instability of quantum bits often resulting in erroneous states. While there are schemes in place to encode logical qubit states, such as repetition codes, the very quantum nature of these qubits makes it impossible to directly observe their quantum states without causing it to decohere. To circumvent this, parity measurements of localized groups of qubits, so-called syndrome measurements, can be performed as is the case in the surface code. The encoding leads to improved stability and error resistance of the encoded logical qubit. The challenge of decoding the surface code in the presence of potential errors still remains: Multiple possible error configurations can lead to the same observed syndrome state, thus making the decoding task non-trivial. This has been addressed with different approaches such as the utilization of decoder agents trained via deep learning. In this study, we deploy techniques from the realm of reinforcement learning such as Deep Q-learning, Proximal Policy Optimization, and Hindsight learning to train agents capable of decoding errors on the surface code. To better reflect a realistic setting, we also acknowledge the possibility of erroneous syndrome measurements as part of the training. The entirety of these syndrome measurements constitutes the observable state and introducing measurement errors breaks the Markov assumption which is central to many reinforcement learning algorithms and leaves us with a partially observable Markov decision process (POMDP). To deal with this, we introduce the dimension of time to our problem formulation by keeping track of the evolution of both qubits and syndromes. Our work includes a brand new state formulation for the syndrome evolution and utilizes different strategies to train agents on this newly-formulated problem.
Keywords: Deep Learning; Reinforcement Learning; Quantum Error Correction; Surface Code; Quantum Bits