Unifying gate-synthesis and magic state distillation

TL;DR

This paper presents a unified approach combining magic state distillation and gate synthesis, reducing resource costs by achieving quadratic error suppression in a single step.

Contribution

A novel framework that integrates distillation and synthesis, enabling fewer distillation rounds and resource savings in quantum circuit implementation.

Findings

Achieves quadratic error suppression in a single step

Reduces the number of distillation rounds needed

Maintains the same T gate count as traditional methods

Abstract

The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T gate, an essential quantum logic gate. Subsequently, gate synthesis intersperses many T gates with Clifford gates to realise a desired circuit. We introduce a unified framework that implements one round of distillation and multi-qubit gate synthesis in a single step. Typically, our method uses the same number of T gates as conventional synthesis, but with the added benefit of quadratic error suppression. Because of this, one less round of magic state distillation needs to be performed, leading to significant resource savings.