Quantum advantage of unitary Clifford circuits with magic state inputs

TL;DR

This paper demonstrates that unitary Clifford circuits with magic state inputs exhibit quantum advantage by being hard to simulate classically, supported by complexity-theoretic conjectures and an extended Gottesman-Knill theorem, with practical implementation benefits.

Contribution

It establishes the classical hardness of simulating CM circuits and extends the Gottesman-Knill theorem to universal computation with mixed inputs.

Findings

CM circuits are hard to classically simulate under certain complexity assumptions.

An extension of the Gottesman-Knill theorem applies to universal Clifford circuits with mixed inputs.

Discussion of practical advantages for implementing CM circuits.

Abstract

We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative error (assuming PH non-collapse), and also up to additive error under plausible average-case hardness conjectures. Unlike other such known classes, a broad variety of possible conjectures apply. Along the way we give an extension of the Gottesman-Knill theorem that applies to universal computation, showing that for Clifford circuits with joint stabiliser and non-stabiliser inputs, the stabiliser part can be eliminated in favour of classical simulation, leaving a Clifford circuit on only the non-stabiliser part. Finally we discuss implementational advantages of CM circuits.