Decoders and circuits for practical quantum error correction

Abstract

In this thesis, we explore practical areas in the theory of quantum error correction that have become especially relevant in light of recent experimental advances. We address the question of whether classical decoding calculations, which are required in order to detect, track and correct errors, can be performed in real-time at a sufficient pace to keep up with the quantum clock speed. Our investigation includes consideration of practical details, such as the communication bandwidth that is required for the classical decoder to interact with the quantum control hardware. We consider the technique of post-selection, which is often used to boost logical performance in small-scale experimental demonstrations of quantum error correction. In particular, we address the common criticism that post-selection is not scalable, and investigate applications of post-selection for medium-scale state preparation circuits, which will continue to be relevant in large-scale quantum computers. Finally, we address the problem of circuit design, whereby theoretical constructs from quantum error correction are translated into a gate-level set of instructions that can be executed on hardware, and in particular we search for time-optimal circuits for detecting errors in topological codes.