Memory-assisted decoder for approximate Gottesman-Kitaev-Preskill codes

TL;DR

This paper introduces a quantum error correction protocol for approximate GKP states that enhances protection through multiple syndrome extraction rounds and Bayesian estimation, with bounded total displacement error and simplified circuit implementation.

Contribution

It presents a novel multi-round error correction scheme for GKP codes that improves error protection and simplifies circuit requirements by integrating squeezing into auxiliary state preparation.

Findings

Multiple rounds of syndrome extraction improve error protection.

Total displacement error is bounded by 2√π after correction.

Circuit recompilation reduces squeezing operations to simpler transformations.

Abstract

We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys. Rev. A {\bf 73}, 012325 (2006)]. We show that combining multiple rounds of error-syndrome extraction with Bayesian estimation offers enhanced protection of GKP-encoded qubits over comparible single-round approaches. Furthermore, we show that the expected total displacement error incurred in multiple rounds of error followed by syndrome extraction is bounded by $2\sqrt{\pi}$. By recompiling the syndrome-extraction circuits, we show that all squeezing operations can be subsumed into auxiliary state preparation, reducing them to beamsplitter transformations and quadrature measurements.