Non-Uniform Code Concatenation for Universal Fault-Tolerant Quantum Computing

TL;DR

This paper introduces a non-uniform code concatenation method for fault-tolerant quantum computing, enabling universality without magic state distillation by combining specific quantum error-correcting codes.

Contribution

It proposes a novel non-uniform concatenation approach of quantum codes, improving fault-tolerance and universality in quantum computing.

Findings

Achieves universal fault-tolerant gates without magic state distillation.

Constructs 49-qubit and 47-qubit codes with enhanced error correction.

Demonstrates non-uniform concatenation as a viable alternative to existing methods.

Abstract

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state distillation, code switching or code concatenation in order to achieve universality. In this paper we propose an alternative approach for universal fault-tolerant quantum computing mainly based on the code concatenation approach proposed in [PRL 112, 010505 (2014)] but in a non-uniform fashion. The proposed approach is described based on non-uniform concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code as well as the 5-qubit code with the 15-qubit Reed-Muller code, which lead to two 49-qubit and 47-qubit codes, respectively. These codes can correct any arbitrary single physical error with the ability to perform a universal set of fault-tolerant gates, without using magic state distillation.