Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle

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We use Pontryagin's minimum principle to optimize variational quantum algorithms.

• We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian decoherence.
• Our findings support the choice of evolution ansatz in the recently proposed Quantum Approximate Optimization Algorithm.
• Focusing on the Sherrington-Kirkpatrick spin-glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian.