Using a Kerr interaction for GKP magic state preparation

TL;DR

This paper proposes a novel method for preparing GKP magic states using a Kerr interaction to implement a logical gate, enhancing fidelity with error correction and feasible circuit QED implementation.

Contribution

It introduces a Kerr-based non-Gaussian unitary for GKP magic state preparation, avoiding auxiliary qubits and compatible with energy constraints.

Findings

Kerr interaction realizes a logical $\

Fidelity improved with SBS error correction and post-selection.

Proposed circuit QED implementation for Kerr interaction.

Abstract

Magic state distillation and injection is a promising strategy towards universal fault tolerant quantum computation, especially in architectures based on the bosonic Gottesman-Kitaev-Preskill (GKP) codes where non-Clifford gates remain challenging to implement. Here we address GKP magic state preparation by studying a non-Gaussian unitary mediated by a Kerr interaction which realizes a logical gate $\sqrt{H}_L$ for square GKP codes. This gate does not directly involve an auxiliary qubit and is compatible with finite energy constraints on the code. Fidelity can be further enhanced using the small-Big-small (SBS) error correction protocol and post-selection, making the scheme robust against a single photon loss event. We finally propose a circuit QED implementation to operate the Kerr interaction.