Quantum error correction using squeezed Schr\"odinger cat states

TL;DR

This paper introduces a new bosonic quantum error correction code based on squeezed Schr"odinger cat states, which enhances protection against both dephasing and particle loss errors in quantum harmonic oscillators.

Contribution

The authors develop and analyze a squeezed cat code that improves error correction capabilities over traditional cat codes, including protocols for generation, gates, and optimal recovery.

Findings

Squeezed cat states partially correct particle loss errors.

Squeezed cat code outperforms conventional cat code with moderate squeezing.

The protocol is feasible on current quantum hardware.

Abstract

Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schr\"odinger cat codes -- based on the superposition of two coherent states with opposite displacements -- can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e. cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.