An efficient magic state approach to small angle rotations

TL;DR

This paper introduces a low-cost distillation protocol for small angle magic states, significantly reducing resource costs for fault-tolerant quantum rotations, especially for very small angles, compared to existing methods.

Contribution

It presents a novel, compressed distillation routine and a magic state dilution method that together lower the costs of small angle rotations in quantum computing.

Findings

24-fold improvement over gate synthesis for modest angles

Order of magnitude cost reduction for very small angles

Marginal improvement in intermediate angle regime

Abstract

Standard error correction techniques only provide a quantum memory and need extra gadgets to perform computation. Central to quantum algorithms are small angle rotations, which can be fault-tolerantly implemented given a supply of an unconventional species of magic state. We present a low-cost distillation routine for preparing these small angle magic states. Our protocol builds on the work of Duclos-Cianci and Poulin [Phys. Rev. A, 91, 042315 (2015)] by compressing their circuit. Additionally, we present a method of diluting magic states that reduces costs associated with very small angle rotations. We quantify performance by the expected number of noisy magic states consumed per rotation, and compare with other protocols. For modest size angles, our protocols offer a factor 24 improvement over the best known gate synthesis protocols and a factor 2 over the Duclos-Cianci and Poulin protocol. For very small angle rotations, the dilution protocol dramatically reduces costs, giving several orders magnitude improvement over competitors. There also exists an intermediary regime of small, but not very small, angles where our approach gives a marginal improvement over gate synthesis. We discuss how different performance metrics may alter these conclusions.