Systematic construction of digital autonomous quantum error correction for state preparation and error suppression via conditional Gaussian operations

TL;DR

This paper introduces a method for autonomous quantum error correction in continuous-variable systems using conditional Gaussian operations, enabling robust state preparation and error suppression without explicit measurements.

Contribution

It proposes a nullifier-based digital autonomous QEC scheme with explicit gate decompositions, demonstrating its effectiveness for state preparation and error suppression in realistic conditions.

Findings

Successfully prepares non-Gaussian resource states for quantum computing.

Autonomously suppresses dephasing errors in cat states.

Analyzes resource trade-offs and performance under imperfections.

Abstract

In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome measurements and feedback. Here, we propose a nullifier-based digital autonomous QEC enabled by conditional Gaussian operations. By designing jump operators for target nullifiers and compiling the resulting Lindbladian into a Trotterized sequence of elementary conditional Gaussian operations, we demonstrate two use cases: (i) deterministic preparation of non-Gaussian resource states for universal computation, including finitely squeezed cubic phase states and approximate trisqueezed states, and (ii) autonomous suppression of dephasing error for cat and squeezed cat states. We provide explicit gate decompositions for the required conditional Gaussian operations and numerically evaluate the performance under realistic imperfections, including photon loss in the bosonic mode and ancillary-qubit decoherence. Our results clarify the resource requirements and trade-offs, such as circuit depth, time-step choices, and the required set of conditional Gaussian operations, for scalable, gate-level implementations of autonomous state preparation and error suppression.