Construction of Bias-preserving Operations for Pair-cat Code

TL;DR

This paper develops bias-preserving operations for pair-cat codes, enabling hardware-efficient fault-tolerant quantum computation that corrects both bosonic loss and dephasing errors through continuous quantum error correction.

Contribution

It generalizes bias-preserving operations from cat codes to pair-cat codes, making them compatible with continuous error correction for multiple error types.

Findings

Designed bias-preserving gates for pair-cat codes.

Demonstrated compatibility with continuous quantum error correction.

Enhanced robustness against bosonic loss and dephasing errors.

Abstract

Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can achieve hardware-efficient fault-tolerant quantum computation with a more favorable error threshold. Distinct from two-level physical systems, multi-level systems (such as harmonic oscillators) can achieve a desirable set of bias-preserving quantum operations while using continuous engineered dissipation or Hamiltonian protection to stabilize to the encoding subspace. For example, cat codes stabilized with driven-dissipation or Kerr nonlinearity can possess a set of biased-preserving gates while continuously correcting bosonic dephasing error. However, cat codes are not compatible with continuous quantum error correction against excitation loss error, because it is challenging to continuously monitor the parity to correct photon loss errors. In this work, we generalize the bias-preserving operations to pair-cat codes, which can be regarded as a multimode generalization of cat codes, to be compatible with continuous quantum error correction against both bosonic loss and dephasing errors. Our results open the door towards hardware-efficient robust quantum information processing with both bias-preserving operations and continuous quantum error correction simultaneously correcting bosonic loss and dephasing errors.