Cubic phase gates are not suitable for non-Clifford operations on GKP states

TL;DR

This paper demonstrates that the cubic phase gate is ineffective for implementing non-Clifford gates in GKP quantum error correction, challenging previous assumptions about its suitability for universal fault-tolerant quantum computing.

Contribution

It provides a rigorous analysis showing the cubic phase gate's inadequacy for non-Clifford operations on GKP states, contradicting earlier proposals.

Findings

Cubic phase gate performs poorly even with high squeezing

The approach is unsuitable for universal fault-tolerant quantum computation

Challenges the previous belief in the gate's effectiveness

Abstract

With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error correction can be carried out using simple Gaussian operations. Still, non-Clifford gates, required for universality, require non-Gaussian elements. In their original proposal, GKP suggested a particularly simple method of using a single application of the cubic phase gate to perform the logical non-Clifford T-gate. Here we show that this cubic phase gate approach performs extraordinarily poorly, even for arbitrarily large amounts of squeezing in the GKP state. Thus, contrary to common belief, the cubic phase gate is not suitable for achieving universal fault-tolerant quantum computation with GKP states.