Variational Quantum Algorithms with Tunable Classical Optimization Costs

Variational quantum circuits are a popular framework for building quantum computing algorithms. Most variational quantum algorithms utilize classical optimization to set variational parameters, a method that is typically computationally expensive or even intractable due to barren plateaus. Approaches that eschew classical optimization in favor of closed-form parameter setting, such as the feedback-based FALQON algorithm inspired by quantum Lyapunov control, mitigate this issue but typically prescribe long gate sequences that can be difficult to implement with high fidelity on current quantum devices. In this talk, we present a new type of variational algorithm inspired by model predictive control that enables a tunable tradeoff between classical optimization effort and variational circuit depth. We prove that, with an appropriate classical optimization formulation, it performs at least as well as Lyapunov-based approaches such as FALQON, and present numerical illustrations demonstrating the potential for significant performance improvements in terms of gate depth required for convergence. We leverage a combination of a reduced-order model (e.g., Pauli propagation) and classical shadows to make the classical optimization component of the algorithm tractable. This algorithm demonstrates an ideal setting for integrating high performance computing with quantum computing, opening new possibilities for scalable hybrid algorithms.