  Supervised time-series classification garners widespread interest because of
its applicability throughout a broad application domain including finance,
astronomy, biosensors, and many others. In this work, we tackle this problem
with hybrid quantum-classical machine learning, deducing pairwise temporal
relationships between time-series instances using a time-series Hamiltonian
kernel (TSHK). A TSHK is constructed with a sum of inner products generated by
quantum states evolved using a parameterized time evolution operator. This sum
is then optimally weighted using techniques derived from multiple kernel
learning. Because we treat the kernel weighting step as a differentiable convex
optimization problem, our method can be regarded as an end-to-end learnable
hybrid quantum-classical-convex neural network, or QCC-net, whose output is a
data set-generalized kernel function suitable for use in any kernelized machine
learning technique such as the support vector machine (SVM). Using our TSHK as
input to a SVM, we classify univariate and multivariate time-series using
quantum circuit simulators and demonstrate the efficient parallel deployment of
the algorithm to 127-qubit superconducting quantum processors using quantum
multi-programming.
