Error-Robust Quantum Signal Processing using Rydberg Atoms

TL;DR

This paper demonstrates that quantum signal processing protocols can be made error-robust on Rydberg atom platforms, enabling high-fidelity quantum algorithms with reduced error scaling and practical implementation using existing experimental parameters.

Contribution

It introduces an error-robust quantum signal processing method tailored for Rydberg atoms, improving error scaling and feasibility of complex quantum algorithms.

Findings

QSP protocols can be made error-robust with slower error scaling.

Up to a hundred gates can be implemented with constant error probability.

The approach significantly outperforms fourth-order product-formula protocols.

Abstract

Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg atom arrays in implementing quantum algorithms depends crucially on their robustness to gate-induced errors. Here we show that, for an idealized biased error model based on Rydberg atom dynamics, the implementation of QSP protocols can be made error-robust, in the sense that the asymptotic scaling of the gate-induced error probability is slower than that of gate complexity. Moreover, using experimental parameters reported in the literature, we show that QSP iterates made out of up to a hundred gates can be implemented with constant error probability. To showcase our approach, we provide a concrete blueprint to implement QSP-based near-optimal Hamiltonian simulation on the Rydberg atom platform. Our protocol substantially improves both the scaling and the overhead of gate-induced errors in comparison to those protocols that implement a fourth-order product-formula.