Quantum simulation with sum-of-squares spectral amplification

TL;DR

This paper introduces SOSSA, a novel spectral amplification framework that enhances quantum simulation efficiency for low-energy problems, demonstrating significant speedups in complex models like the Sachdev-Ye-Kitaev system.

Contribution

The paper presents SOSSA, a new spectral amplification method that improves quantum simulation algorithms for energy and phase estimation, with demonstrated asymptotic speedups in strongly correlated systems.

Findings

SOSSA achieves asymptotic speedups over generic methods.

Demonstrates improvements in simulating the Sachdev-Ye-Kitaev model.

Reinforces prior results on quantum chemistry systems.

Abstract

We present sum-of-squares spectral amplification (SOSSA), a framework for improving quantum simulation relevant to low-energy problems. We show how SOSSA can be applied to problems like energy and phase estimation and provide fast quantum algorithms for these problems that significantly improve over prior art. To illustrate the power of SOSSA in applications, we consider the Sachdev-Ye-Kitaev model, a representative strongly correlated system, and demonstrate asymptotic speedups over generic simulation methods by a factor of the square root of the system size. Our results reinforce those observed in [G.H. Low \textit{et al.}, arXiv:2502.15882 (2025)], where SOSSA was used to achieve state-of-the-art gate costs for phase estimation of real-world quantum chemistry systems.