Bosonic quantum Fourier codes

TL;DR

This paper introduces a bosonic quantum Fourier code that encodes quantum information in higher-dimensional systems using inverse quantum Fourier transform, offering good error correction and a feasible universal gate set.

Contribution

It presents a novel bosonic code based on the Fourier transform of a finite subgroup of $U(2)$, enhancing error correction and control in quantum computing.

Findings

The two-mode Fourier cat code exhibits strong error correction properties.

It supports an experimentally-friendly universal gate set.

The approach simplifies fault-tolerant quantum architecture.

Abstract

While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first level of redundancy and error correction that simplifies the overall fault-tolerant architecture. A challenge then is to ensure universal control over the encoded qubits. Here, we explore an approach where information is encoded in an irreducible representation of a finite subgroup of $U(2)$ through an inverse quantum Fourier transform. We illustrate this idea by applying it to the real Pauli group $\langle X, Z\rangle$ in the bosonic setting. The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set that we discuss in detail.