A decision-theoretic framework for quantum error correction

The reliability of quantum computers critically depends on the ability to detect and correct errors arising from imperfect hardware and environmental noise. The field of quantum error correction provides the tools to achieve this by encoding quantum information according to specific rules, so that redundancy in the encoding allows the original information to be restored in case of errors. Among the various codes, the surface code represents the state of the art due to its unique features. The central problem in quantum error correction is decoding, which refers to choosing the most appropriate correction based on non-destructive measurements of the encoded state, called syndromes. Most decoding strategies in the literature focus on immediate correction of the most probable error within a given class. A novel approach, however, focuses instead on the long-term performance of error correction, assuming it can be maximized by abandoning the principle of immediate correction of the most probable error and, instead, formulating decoding as a decisiontheoretic problem and using control theory techniques to determine which corrections to apply, in particular reinforcement learning. This thesis builds on this line of research by reframing the decoding of surface codes as a partially observable Markov decision process (POMDP). This formulation allows the incorporation of user-defined utility functions, which can reflect preferences such as tolerance for delays in result delivery or the evaluation of damage caused by incorrect decoding. It also enables the explicit modeling of errors in syndrome measurements. To convert the history of syndrome obtained from surface code measurements into a format compatible with a POMDP treatment for real-time operation, we define an approximate computational strategy. This algorithm iteratively updates a set of relevant probability distributions over the errors using the rolling syndrome data in polynomial time. This allows to perform a mapping between decoding and a POMDP that is useful for decoding at run-time. We define workflows to solve the decoding problem by training a decoding agent using reinforcement learning. Our workflows address all phases of the decoder agent’s lifecycle, including training, testing, updating, and run-time deployment. In the end we have a complete abstract framework, ready to be implemented in practical scenarios.