Adaptive Optimal Control of Entangled Qubits

Developing fast, robust, and accurate methods for optimal control of quantum systems comprising interacting particles is one of the most active areas of current science. Although a valuable repository of algorithms is available for numerical applications in quantum control, the high computational cost is somewhat overlooked. Here we present a fast and accurate optimal control algorithm for systems of interacting qubits, QOALA (Quantum Optimal control by Adaptive Low-cost Algorithm), that offers O(M^2) speed-up for an M-qubit system, compared to the state-of-the-art exact methods, without compromising overall accuracy of the optimal solution. The method is general and compatible with diverse Hamiltonian structures. The proposed approach uses inexpensive low-accuracy approximations of propagators far from the optimum, adaptively switching to higher accuracy, higher-cost propagators when approaching the optimum. Additionally, the utilisation of analytical Lie algebraic derivatives that do not require computationally expensive matrix exponential brings even better performance. Complete mathematical treatment of the subject using a general formalism, along with a diverse range of demonstrations in the context of nuclear magnetic resonance (NMR), are presented.