  Quantum machine learning has emerged as a promising utilization of near-term
quantum computation devices. However, algorithmic classes such as variational
quantum algorithms have been shown to suffer from barren plateaus due to
vanishing gradients in their parameters spaces. We present an approach to
quantum algorithm optimization that is based on trainable Fourier coefficients
of Hamiltonian system parameters. Our ansatz is exclusive to the extension of
discrete quantum variational algorithms to analog quantum optimal control
schemes and is non-local in time. We demonstrate the viability of our ansatz on
the objectives of compiling the quantum Fourier transform and preparing ground
states of random problem Hamiltonians. In comparison to the temporally local
discretization ans\"atze in quantum optimal control and parameterized circuits,
our ansatz exhibits faster and more consistent convergence. We uniformly sample
objective gradients across the parameter space and find that in our ansatz the
variance decays at a non-exponential rate with the number of qubits, while it
decays at an exponential rate in the temporally local benchmark ansatz. This
indicates the mitigation of barren plateaus in our ansatz. We propose our
ansatz as a viable candidate for near-term quantum machine learning.
