Fast, high precision dynamics in quantum optimal control theory

Abstract

Quantum optimal control theory is becoming increasingly crucial as quantum devices become more precise, but the need to quickly optimize these systems classically remains a significant bottleneck in their operation. Here we present a new theoretical quantum control framework for much faster optimization than the state of the art by replacing standard time propagation with a product of short-time propagators, each calculated using the Magnus expansion. The derived formulas for exact series terms and their gradients, based on earlier approximate integrals in a simulation setting, allow us to subsume the high cost of calculating commutators and integrals as an initial overhead. This provides an order of magnitude speedup for all subsequent dynamical trajectories used in control and noise sampling for both quantum simulation and optimal control.

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…Similarly, faster optimization is possible by generalizing Krotov's method to second order in all derivatives [520]. Further speed-ups are possible by replacing standard time propagation with a product of shorttime propagators [160].…”

The Challenges of Inventory Management in Medical Supply Chain

“…Furthermore, CT is useful for comprehending supply networks' dynamic behaviour. In order to perform dynamical operations such as state-to-state transfers, unitary gate synthesis, or the creation of a dispersion relation in closed and open systems, control optimum also permits the tailoring of externally applied control fields (Dalgaard & Motzoi, 2022). As per the theory, the control problem should be formulated to minimize a cost function concerning a group of control fields used to direct the system during a control procedure (Zemzam et al, 2017).…”