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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., 18 pages, 6 figures

Additional file 1: Supplementary information.

In this paper we study the potential of gene-protein interaction networks to store input-output patterns. The central question in this study concerns the memory capacity of a network of a given number of genes and proteins, which interact according to a linear state space model with external inputs. Here it is assumed that to a certain combination of inputs there exists an optimal state of the system, i.e., values of the gene expressions and protein levels, that has been attained externally, e.g., through evolutionary learning. Given such a set of learned optimal input-output patterns, the design question here is to find a sparse and hierarchical network structure for the gene-protein interactions and the gene-input couplings. This problem is formulated as an optimization problem in a linear programming setting. Numerical analysis shows that there are clear scale-invariant continuous second-order phase transitions for the network sparsity as the number of patterns increases. These phase transitions divide the system in three regions with different memory characteristics. It is possible to formulate simple scaling rules for the behavior of the network sparsity. Finally, numerical experiments show that these patterns are stable within a certain finite range around the patterns.