Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations

TL;DR

This paper establishes precise noise thresholds for single-qubit non-stabilizer gates in quantum circuits with perfect stabilizer operations, delineating when such gates enable universal quantum computation.

Contribution

It provides the first tight depolarizing noise thresholds for all unitary single-qubit gates, based on the Clifford polytope, clarifying their role in quantum computational universality.

Findings

Thresholds are determined by the Clifford polytope.

All unitary single-qubit gates have a specific noise threshold for universality.

The thresholds are tight and contrast with non-stabilizer state scenarios.

Abstract

We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove that for all unitary single-qubit gates there exists a tight depolarizing noise threshold that determines whether the gate enables universal quantum computation or if the gate can be simulated by a mixture of Clifford gates. This exact threshold is determined by the Clifford polytope spanned by the 24 single-qubit Clifford gates. The result is in contrast to the situation wherein non-stabilizer qubit states are used; the thresholds in that case are not currently known to be tight.