Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

TL;DR

This paper presents a new efficient method for approximating any single-qubit quantum channel using fewer CNOT gates, leveraging a decomposition into quasiextreme channels, which is more practical for current quantum experiments.

Contribution

It introduces a novel decomposition strategy for single-qubit channels that significantly reduces the required CNOT gates compared to previous methods.

Findings

Requires only one CNOT gate for approximation

Reduces complexity from up to 20 CNOT gates to just one

Enables more practical implementation of quantum channel simulation

Abstract

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments.