I will give an overview of what I see as some of the most important future directions in the
theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the …

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and
good code distance scaling, potentially enabling low-overhead fault-tolerant quantum …

Quantum error correction is an indispensable ingredient for scalable quantum computing. In
this Perspective we discuss a particular class of quantum codes called “quantum low-density …

In this perspective we discuss conditions under which it would be possible for a modest fault-
tolerant quantum computer to realize a runtime advantage by executing a quantum …

Vast numbers of qubits will be needed for large-scale quantum computing because of the
overheads associated with error correction. We present a scheme for low-overhead fault …

We show that belief propagation combined with ordered statistics post-processing is a
general decoder for quantum low-density parity-check codes constructed from the …

Quantum low density parity check (LDPC) codes may provide a path to build low-overhead
fault-tolerant quantum computers. However, as general LDPC codes lack geometric …

Standard approaches to quantum error correction for fault-tolerant quantum computing are
based on encoding a single logical qubit into many physical ones, resulting in asymptotically …

In this work, we study the single-shot performance of higher-dimensional hypergraph
product codes decoded using belief propagation and ordered-statistics decoding [P …

Single-shot error correction corrects data noise using only a single round of noisy
measurements on the data qubits, removing the need for intensive measurement repetition …