Squeezed-vacuum bosonic codes

TL;DR

This paper introduces a new family of bosonic quantum error-correcting codes called squeezed-vacuum codes, which leverage rotation symmetry and squeezed vacuum states to protect against loss and dephasing noise, with practical implementation strategies.

Contribution

The paper presents a novel class of error-correcting codes based on squeezed vacuum states, including simple preparation circuits and performance analysis against noise channels.

Findings

Codes improve loss tolerance with more squeezed-vacuum states.

Performance evaluated using Knill-Laflamme violation function.

Benchmarking against cat codes shows competitive error correction.

Abstract

We introduce a family of bosonic quantum error-correcting codes built as a rotation-symmetric superposition of squeezed vacuum states, which promise protection against both loss and dephasing noise channels. The robustness of these "squeezed-vacuum codes" arises from being arranged at evenly spaced angles in phase-space, and simultaneously in evenly spaced photon-number support $n \equiv {2k} \! \pmod {2m}$. We present simple preparation circuits: a two-legged code using a Hadamard-conditional-squeezing-Hadamard sequence on an ancilla qubit, and for general "$m$-legged" codewords using sequences of conditional rotations. The performance of these codes is evaluated against loss and dephasing noises using the Knill-Laflamme violation function and benchmarked against cat codes. As the number $m$ of squeezed-vacuum states in a code increases, the code exhibits improved loss tolerance at the cost of higher dephasing sensitivity. We outline implementations in circuit QED and trapped-ion platforms, where high-fidelity Gaussian operations and conditional controls are available or under active development. These results help establish squeezed-vacuum codes as practical, hardware-ready, members of the bosonic codes class.