Fault-tolerant fermionic quantum computation based on color code

TL;DR

This paper demonstrates that fermionic quantum computation can be made universal and fault-tolerant by encoding logical Majorana fermions in physical Majorana fermions using a color code, with a threshold of about 0.8%.

Contribution

It introduces a method to achieve fault-tolerant fermionic quantum computation using color codes, expanding the scope of quantum error correction.

Findings

Fault-tolerant threshold is approximately 0.8%.

Universal set of fault-tolerant operations on logical Majorana fermions demonstrated.

Fermionic quantum computation can be protected using quantum error correction.

Abstract

An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with the qubit quantum computation, the fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g. molecules. In this paper, we show that the fermionic quantum computation can be universal and fault-tolerant if we encode logical Majorana fermions in physical Majorana fermions. We take a color code as an example to demonstrate the universal set of fault-tolerant operations on logical Majorana fermions, and we numerically find that the fault-tolerance threshold is about 0.8%.