Quantum technologies have the potential to solve certain computationally hard problems
with polynomial or super-polynomial speedups when compared to classical methods …

This article provides an introduction to surface code quantum computing. We first estimate
the size and speed of a surface code quantum computer. We then introduce the concept of …

The manipulation of topologically ordered phases of matter to encode and process quantum
information forms the cornerstone of many approaches to fault-tolerant quantum computing …

Quantum error correction is believed to be essential for scalable quantum computation, but
its implementation is challenging due to its considerable space-time overhead. Motivated by …

The construction of a quantum computer remains a fundamental scientific and technological
challenge because of the influence of unavoidable noise. Quantum states and operations …

In order to build a large scale quantum computer, one must be able to correct errors
extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli …

We propose a new model of quantum computation comprised of low-weight measurement
sequences that simultaneously encode logical information, enable error correction, and …

The color code is a topological quantum error-correcting code supporting a variety of
valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code …

Two-dimensional color codes are a promising candidate for fault-tolerant quantum
computing, as they have high encoding rates, transversal implementation of logical Clifford …

Consider a 2-D square array of qubits of extent $ L\times L $. We provide a proof that the
minimum weight perfect matching problem associated with running a particular class of …