# Quantum computing with rotation-symmetric bosonic codes

## TL;DR

This paper introduces bosonic rotation codes, especially number-phase codes like cat and binomial codes, and presents a universal quantum computing scheme with error correction and fault-tolerance features.

## Contribution

It proposes a universal quantum computing scheme for rotation-symmetric bosonic codes, including a code-agnostic entangling gate and a teleportation-based error correction method.

## Key findings

- Error correction fidelity close to optimal under ideal conditions
- Universal gate set demonstrated for number-phase codes
- Fault-tolerant scheme combining rotation codes with Bacon-Shor codes

## Abstract

Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase codes--which includes the well-known cat and binomial codes, among many others. The entangling gate in our scheme is code-agnostic and can be used to interface different rotation-symmetric encodings. In addition to a universal set of operations, we propose a teleportation-based error correction scheme that allows recoveries to be tracked entirely in software. Focusing on cat and binomial codes as examples, we compute average gate fidelities for error correction under simultaneous loss and dephasing noise and show numerically that the error-correction scheme is close to optimal for error-free ancillae and ideal measurements. Finally, we present a scheme for fault-tolerant, universal quantum computing based on concatenation of number-phase codes and Bacon-Shor subsystem codes.