Low-overhead Magic State Circuits with Transversal CNOTs

TL;DR

This paper introduces low-overhead fault-tolerant circuits for magic states using transversal CNOTs, significantly reducing CNOT depth and qubit count, thereby enhancing the efficiency of fault-tolerant quantum computation.

Contribution

It presents novel algorithms to recompile and simplify multi-qubit phase rotation circuits, enabling fault-tolerant CCZ, CS, and T state preparation with minimal resource overhead.

Findings

Reduced CNOT depth and qubit count for magic state circuits

Minimal T-depth achievable within given workspace constraints

Potential for broader application in fault-tolerant quantum protocols

Abstract

With the successful demonstration of transversal CNOTs in many recent experiments, it is the right moment to examine its implications on one of the most critical parts of fault-tolerant computation -- magic state preparation. Using an algorithm that can recompile and simplify a circuit of consecutive multi-qubit phase rotations, we manage to construct fault-tolerant circuits for CCZ, CS and T states with much lower CNOT depths and qubit counts than before and minimal T-depth for the given workspace. These circuits can play crucial roles in fault-tolerant computation with transversal CNOTs, and we hope that the algorithms and methods developed in this paper can be used to further simplify other protocols in similar contexts.