Quantum computing for accelerating cross-correlations intensive applications in signal processing

TL;DR

This paper introduces two quantum algorithms to compute and store cross-correlations and implement the expectation maximization maximum likelihood algorithm, achieving a quadratic speed-up over classical methods in signal processing applications.

Contribution

It presents novel quantum algorithms for cross-correlation computation and maximum likelihood estimation, filling a gap in quantum signal processing research.

Findings

Quantum algorithms for cross-correlation and EM ML are proposed.

The quantum EM ML algorithm has a quadratic speed-up.

Potential for significant acceleration in signal processing tasks.

Abstract

Despite their importance as subfields of mathematics and engineering, signal and image processing have not received much attention in the field of quantum computation. Cross-correlations are instrumental to all the aforementioned fields. In this article we help fill this void by providing two quantum algorithms, one for computing and storing cross-correlations, and one for implementing the expectation maximization maximum likelihood algorithm. In addition we show that the quantum expectation maximization maximum likelihood algorithm has a quadratic speed-up compared to the classical analog.