Quantum analytic descent

Abstract

Quantum variational algorithms are applicable to a range of tasks and have particular relevance for near-term quantum computers. The approach involves adjusting the parameterised elements of a quantum circuit to minimise the expected energy of the output state with respect to a Hamiltonian encoding the task. Typically the parameter space is navigated by descending the steepest energy gradient at each incremental step; this can become costly as the solution is approached and all gradients vanish. Here we propose an alternative analytic descent mechanism. Given that the variational circuit can be expressed as a (universal) set of Pauli operators, we observe that the energy landscape must have a certain simple form in the local region around any reference point. By fitting an analytic function to the landscape, one can classically analyse that function in order to directly `jump' to the (estimated) minimum, before fitting a more refined function if necessary. We verify this technique using numerical simulations and find that each analytic jump can be equivalent to many thousands of steps of canonical gradient descent.