Error Rates and Resource Overheads of Repetition Cat Qubits

TL;DR

This paper analyzes the error rates and resource costs of repetition cat qubits for fault-tolerant quantum computing, showing promising low error rates achievable with current technology through numerical simulations.

Contribution

It provides a detailed simulation-based analysis of logical error rates and resource overheads for repetition cat qubits, including fault-tolerant gate implementations.

Findings

Low logical error rates are achievable with feasible resources.

Bias-preserving gates enable universal fault-tolerant quantum computation.

Parameters are within reach of near-term circuit QED experiments.

Abstract

We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work, we suggested that the remaining phase-flip error channel could be suppressed using a 1D repetition code. Indeed, using only bias-preserving gates on the cat-qubits, it is possible to build a universal set of fault-tolerant logical gates at the level of the repetition cat qubit. In this paper, we perform Monte-Carlo simulations of all the circuits implementing the protected logical gates, using a circuit-level error model. Furthermore, we analyze two different approaches to implement a fault-tolerant Toffoli gate on repetition cat qubits. These numerical simulations indicate that very low logical error rates could be achieved with a reasonable resource overhead, and with parameters that are within the reach of near-term circuit QED experiments.