Implementation-independent sufficient condition of the Knill-Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation

TL;DR

This paper proves that the Knill-Laflamme condition is sufficient for protecting logical qudits using engineered dissipation, providing a scalable method for autonomous quantum error correction applicable to bosonic codes.

Contribution

It establishes a general, implementation-independent criterion for autonomous quantum error correction based on the Knill-Laflamme condition, with explicit error scaling analysis.

Findings

Error suppression scales with dissipation strength and time

Knill-Laflamme condition suffices for Markovian noise protection

Application demonstrated with bosonic binomial codes

Abstract

Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental error operators should act trivially on a subspace, which then becomes the code subspace, is sufficient for logical qudits to be protected against Markovian noise. It is proven that the error caused by the total Lindbladian evolution in the code subspace can be suppressed up to very long times in the limit of large engineered dissipation, by explicitly deriving how the error scales with both time and engineered dissipation strength. To demonstrate the potential of our approach for applications, we implement our general theory with binomial codes, a class of bosonic error-correcting codes, and outline how they can be implemented in a fully autonomous manner to protect against photon loss in a microwave cavity.