A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations

TL;DR

This paper introduces a novel state distillation protocol for implementing arbitrary single-qubit rotations that reduces sequence length and resource requirements compared to traditional methods, while maintaining robustness to noise.

Contribution

The paper proposes a new state distillation-based protocol that improves the efficiency of approximating single-qubit rotations beyond the Solovay-Kitaev method.

Findings

Reduces the exponent c from ~3.97 to between 1.12 and 2.27.

Lowers the length of the approximating sequence.

Decreases the number of resource states needed.

Abstract

An important task required to build a scalable, fault-tolerant quantum computer is to efficiently represent an arbitrary single-qubit rotation by fault-tolerant quantum operations. Traditionally, the method for decomposing a single-qubit unitary into a discrete set of gates is Solovay-Kitaev decomposition, which in practice produces a sequence of depth O(\log^c(1/\epsilon)), where c~3.97 is the state-of-the-art. The proven lower bound is c=1, however an efficient algorithm that saturates this bound is unknown. In this paper, we present an alternative to Solovay-Kitaev decomposition employing state distillation techniques which reduces c to between 1.12 and 2.27, depending on the setting. For a given single-qubit rotation, our protocol significantly lowers the length of the approximating sequence and the number of required resource states (ancillary qubits). In addition, our protocol is robust to noise in the resource states.