# Designing good bosonic quantum codes via creating destructive interference

## TL;DR

This paper introduces a novel approach to designing bosonic quantum error-correcting codes by exploiting destructive interference through phase manipulation, leading to improved error suppression in continuous-variable quantum systems.

## Contribution

It proposes using phase degrees of freedom in basis state amplitudes to create destructive interference, enhancing code performance against excitation loss and Kerr effects.

## Key findings

- Phase manipulation significantly reduces decoherence in bosonic codes.
- Tailored recovery strategies improve error correction effectiveness.
- The approach applies to various bases and multi-qubit codes.

## Abstract

Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states in the error-relevant basis. Here, we propose utilizing the phase degree of freedom in basis state probability amplitudes to devise codes that feature destructive interference, and thus reduced overlap, between error codewords. To showcase, we first consider the correction of excitation loss using single-mode codes with Fock-space parity structure and show that, with a tailored "two-level" recovery, altering the signs of probability amplitudes can significantly suppress decoherence. We then study the joint channel of excitation loss and Kerr effect, and show the critical role of nontrivial phase for optimal quantum codes for such intricate yet important channels. The principle is extended to improve bosonic codes defined in other bases and multi-qubit codes, showing its wide applicability in quantum error correction.