Impact of finite squeezing on near-term quantum computations using GKP qubits

TL;DR

This paper simulates measurement-based quantum computation with GKP qubits, showing how finite squeezing affects performance and identifying a threshold around 10 dB for quantum advantage in Grover's algorithm.

Contribution

First detailed simulation of GKP-based measurement quantum computation using FMPS, explicitly modeling finite squeezing effects and benchmarking performance.

Findings

Strong agreement with analytical estimates at high squeezing levels

Identified a 10 dB squeezing threshold for quantum advantage in Grover's algorithm

Demonstrated practical quantum computation with over 100 GKP modes

Abstract

We present the first detailed simulation of a measurement based quantum computation based on Gottesman-Kitaev-Preskill (GKP) qubits within a quad-rail lattice (QRL) cluster state involving over 100 GKP modes. This was enabled by the recently developed functional matrix product states (FMPS) framework, with which we simulate continuous-variable (CV) quantum circuits while explicitly modelling intrinsic coherent error sources due to finite squeezing. We perform simulated randomised benchmarking across squeezing levels between 5 and 15 dB and find strong agreement with analytical estimates for high quality GKP qubits. As a demonstration of practical computation, we simulate a three-qubit Grover's algorithm within the QRL and identify a fundamental squeezing threshold -- approximately 10 dB -- beyond which the algorithm outperforms classical probability bounds.