Numerical Synthesis of Arbitrary Multi-Qubit Unitaries with low 𝑇�-Count

Abstract

Quantum gate synthesis based on numerical optimization produces efficient circuits for NISQ (Noisy Intermediate-Scale Quantum) computing by minimizing the num- ber of two-qubit gates. The requirements for fault tolerant quantum computing are significantly different in that some single qubit gates require magic state distillation and gate teleportation, which are resource intensive. Here, We propose an approach to adapt numerical optimization to error corrected quantum circuits by using sequen- tial two-pass multistart numerical optimizaton to reduce the number of 𝑅z gates that must be approximated with Clifford+𝑇 circuits. This technique allows NISQ synthesis based on numerical optimization to be applied to fault-tolerant circuits as well.