Energy-Scaled Zero-Noise Extrapolation for Gottesman-Kitaev-Preskill Code

TL;DR

This paper introduces Energy-Scaled Zero-Noise Extrapolation (ES-ZNE), a method to mitigate finite-energy errors in GKP quantum codes, improving their performance without requiring high squeezing hardware.

Contribution

The paper presents ES-ZNE, a novel error mitigation protocol that uses mean photon number as a tunable noise parameter and extrapolates to ideal infinite-energy conditions.

Findings

ES-ZNE effectively mitigates finite-energy errors in GKP codes.

The method recovers ideal expectation values within numerical uncertainty.

It characterizes the intrinsic performance and error threshold of the GKP code.

Abstract

The performance of Gottesman-Kitaev-Preskill (GKP) codes, an approach to hardware-efficient quantum error correction, is limited by the finite squeezing capabilities of current experimental platforms. To circumvent this hardware demand, we introduce Energy-Scaled Zero-Noise Extrapolation (ES-ZNE), a quantum error mitigation protocol that uses the mean photon number of the GKP code as a tunable effective noise parameter. The protocol measures logical observables at a series of accessible finite energies and extrapolates the results to the ideal, infinite-energy limit using an ansatz based on the code's asymptotic error scaling. Through simulating a GKP qubit under a pure-loss channel, we demonstrate that ES-ZNE successfully mitigates finite-energy errors, recovering the ideal expectation values (within numerical uncertainty) in the shallow-noise regime. Furthermore, by computationally removing artifacts arising from the finite-energy encoding, our method characterizes the intrinsic performance of the ideal GKP code, revealing a sharp error threshold beyond which the code's corrective power diminishes. These results establish ES-ZNE as a practical, software-based strategy for enhancing the performance of near-term bosonic quantum processors, trading sampling overhead for demanding physical resources like high squeezing.