Universal quantum computing with a single arbitrary gate

TL;DR

This paper proposes a method for universal quantum computing using a single arbitrary gate, demonstrating efficient compilation and fault-tolerance improvements for systems with limited degrees of freedom.

Contribution

It introduces an efficient compilation technique for arbitrary gates and shows how to achieve fault-tolerance with minimal gate sets in quantum computing.

Findings

Target gates can be compiled with circuit depth ~log(1/ε).

Gate imperfection can be reduced to 10^{-3} with classical resources.

Error correction further reduces errors by two orders of magnitude.

Abstract

This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number $>2$ is universal. Utilizing a single arbitrary gate for compiling is beneficial for systems with limited degrees of freedom, e.g. the scattering based quantum computing schemes. However, how to efficiently compile the wanted gate with a single arbitrary gate, and finally achieve fault-tolerant quantum computing is unknown. In this work, we show almost any target gate can be compiled to precision $\epsilon$ with a circuit depth of approximately $\log(\epsilon^{-1})$ with an improved brute-force compiling method. Under the assumption of reasonable classical resource, we show the gate imperfection can be lowered to $10^{-3}$. By treating the imperfection as coherent error, we show that the error can be further reduced by roughly two orders of magnitude with a measurement-free quantum error correction method.