Hybrid Quantum Singular Spectrum Decomposition for Time Series Analysis

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.