Quasi-exact quantum computation

TL;DR

This paper introduces quasi-exact quantum error correcting codes that enable a feasible model of quantum computation with quasi-exact universality, supporting transversal gates and fault tolerance for moderate-size algorithms.

Contribution

It proposes the concept of quasi-exact codes, explores their properties, and demonstrates their potential for universal quantum computation with transversal gates.

Findings

Quasi-exact codes can be tuned to exact codes as fixed points.

Quasi-exact universality overcomes the incompatibility with transversality.

Covariant quasi-exact codes support universal transversal gates for SU(d).

Abstract

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding exact codes, serving as its fixed points. The computation with a quasi-exact code cannot realize any logical gate to arbitrary accuracy. To overcome this, the notion of quasi-exact universality is proposed, which makes quasi-exact quantum computation a feasible model especially for executing moderate-size algorithms. We find that the incompatibility between universality and transversality of the set of logical gates does not persist in the quasi-exact scenario. A class of covariant quasi-exact codes is defined which proves to support transversal and quasi-exact universal set of logical gates for $SU(d)$. This work opens the possibility of quantum computation with quasi-exact universality, transversality, and fault tolerance.