An efficient quantum algorithm for spectral estimation

TL;DR

This paper presents a quantum algorithm that significantly accelerates spectral estimation by efficiently determining frequencies and damping factors of signals, outperforming classical methods in speed.

Contribution

The authors introduce a quantum implementation of the matrix pencil method, achieving exponential speedup and developing new techniques for quantum matrix operations.

Findings

Quantum speedup in spectral estimation tasks

Efficient quantum-classical hybrid algorithm design

Logarithmic time complexity in sampling points

Abstract

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well - consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum-classical division of labor: The time-critical steps are implemented in quantum superposition, while an interjacent step, requiring only exponentially few parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.