Combining the synergistic control capabilities of modeling and experiments: Illustration of finding a minimum-time quantum objective

Abstract

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than 99% in an NMR experiment, which is feasible by combining the synergistic capabilities of modelling and experiments operating in tandem. The pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we explore the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches should have broad applications for accelerating the search for optimal quantum controls.

Progress toward favorable landscapes in quantum combinatorial optimization

“…We note that similar findings on overparameterization have appeared in the analysis of quantum control landscapes [21,22,23,24], where in the latter setting, overparameterization takes the form of "sufficient" pulse-level control resources. In fact, VQAs can themselves be considered a form of quantum learning control experiment [25,26,27,28,29], where the control is performed at the quantum circuit level, rather than at the conventional pulse level [24]. Similar findings on the effects of overparameterization have also appeared in the study of classical neural network landscapes [30,31,32].…”

From Pulses to Circuits and Back Again: A Quantum Optimal Control Perspective on Variational Quantum Algorithms

“…If a tractable and accurate model is available, this iteration can be performed numerically. However, it can also be carried out experimentally via learning control[59][60][61][62][63][64], which does not require knowledge of the underlying system model. Instead, at each iteration of such QOC experiments, J[{c i }] is evaluated by first preparing the system in a specified initial state, then evolving it in the presence of applied fields with parametrization {c i }, and finally measuring the observable expectation value(s) needed to estimate J[{c i }].…”

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

“…Spin states in molecules studied by nuclear magnetic resonance (NMR) have been an early proposed platform for quantum computing, and optimal control applied to this platform has been extensively reviewed in [246]. Recent advances include optimized state preparation in a seven-qubit nuclear magnetic resonance system using hybrid quantum-classical approach to quantum optimal control [375] and the near time-optimal preparation of a Bell state where modeling and experiments were operating in tandem [130]. Using optimal control, also a novel class of refocusing pulses for "delayed spin echoes" was developed [39,40], with potential applications in the general field of quantum technology.…”