Low-Overhead Code Concatenation Approaches for Universal Quantum Computation

As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, two approaches for universal fault-tolerant quantum computation, mainly based on code concatenation, are proposed. The proposed approaches outperform code concatenation in terms of both number of qubits and code distance and has also significantly less resource overhead than code switching, magic state distillation and pieceable fault-tolerance at the cost of reducing the effective distance of the concatenated code for implementing non-transversal gates.