Hybrid Quantum Singular Spectrum Decomposition for Time Series Analysis

TL;DR

This paper introduces a hybrid quantum algorithm for time series analysis that leverages quantum computing to perform singular spectrum decomposition more efficiently, demonstrated on brain signals and gravitational wave data.

Contribution

It proposes a quantum-enhanced SSD method using randomized SVD and assesses its feasibility on near-term quantum hardware.

Findings

Quantum SSD can analyze complex time series efficiently.

The method is demonstrated on neural and gravitational wave data.

Randomized SVD improves scalability of the quantum algorithm.

Abstract

Classical data analysis requires computational efforts that become intractable in the age of Big Data. An essential task in time series analysis is the extraction of physically meaningful information from a noisy time series. One algorithm devised for this very purpose is singular spectrum decomposition (SSD), an adaptive method that allows for the extraction of narrow-banded components from non-stationary and non-linear time series. The main computational bottleneck of this algorithm is the singular value decomposition (SVD). Quantum computing could facilitate a speedup in this domain through superior scaling laws. We propose quantum SSD by assigning the SVD subroutine to a quantum computer. The viability for implementation and performance of this hybrid algorithm on a near term hybrid quantum computer is investigated. In this work we show that by employing randomised SVD, we can impose a qubit limit on one of the circuits to improve scalibility. Using this, we efficiently perform quantum SSD on simulations of local field potentials recorded in brain tissue, as well as GW150914, the first detected gravitational wave event.