Quantum Computing with Two-dimensional Conformal Field Theories

TL;DR

This paper explores how two-dimensional conformal field theories can be applied to fault-tolerant quantum computing, introducing a new gapped wavefunction that enables universal quantum computation.

Contribution

It introduces a novel gapped wavefunction based on conformal blocks that generalize the Moore-Read state, facilitating universal quantum computing.

Findings

Calculated higher-dimensional braiding matrices for anyons

Identified gapped states from conformal blocks

Proposed a generalized Moore-Read state for universal quantum computing

Abstract

Conformal field theories have been extremely useful in our quest to understand physical phenomena in many different branches of physics, starting from condensed matter all the way up to high energy. Here we discuss applications of two-dimensional conformal field theories to fault-tolerant quantum computation based on the coset $ SU(2)_1^{\otimes k} / SU(2)_{k}$. We calculate higher-dimensional braiding matrices by considering conformal blocks involving $2N$ anyons, and search for gapped states that can be built from these conformal blocks. We introduce a gapped wavefunction that generalizes the Moore-Read state which is based on the critical Ising model, and show that our generalization leads to universal quantum computing.