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

Understand

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.