Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector

TL;DR

This paper introduces a fault-tolerant error syndrome extraction method in quantum error correction using a bosonic-cat ancilla in a driven nonlinear cavity, reducing overhead and improving robustness against ancilla errors.

Contribution

It proposes a novel approach employing a bosonic-cat qubit in a driven nonlinear cavity for efficient, fault-tolerant error syndrome extraction across various quantum codes.

Findings

Demonstrates fault-tolerant syndrome extraction with a bosonic-cat ancilla.

Shows compatibility with multiple quantum error-correcting codes.

Highlights potential for hardware-efficient quantum error correction.

Abstract

In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat- and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.