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Register a new userAdaptive hybrid optimal quantum control for imprecisely characterized systems
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Optimal quantum control theory carries a huge promise for quantum technology. Its experimental application, however, is often hindered by imprecise knowledge of the its input variables, the quantum systems parameters. We show how to overcome this by Adaptive Hybrid Optimal Control (Ad-HOC). This protocol combines open- and closed-loop optimal by first performing a gradient search towards a near-optimal control pulse and then an experimental fidelity measure with a gradient-free method. For typical settings in solid-state quantum information processing, Ad-Hoc enhances gate fidelities by an order of magnitude hence making optimal control theory applicable and useful.
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Quantum technologies will ultimately require manipulating many-body quantum systems with high precision. Cold atom experiments represent a stepping stone in that direction: a high degree of control has been achieved on systems of increasing complexity, however, this control is still sub-optimal. Optimal control theory is the ideal candidate to bridge the gap between early stage and optimal experimental protocols, particularly since it was extended to encompass many-body quantum dynamics. Here, we experimentally demonstrate optimal control applied to two dynamical processes subject to interactions: the coherent manipulation of motional states of an atomic Bose-Einstein condensate and the crossing of a quantum phase transition in small systems of cold atoms in optical lattices. We show theoretically that these transformations can be made fast and robust with respect to perturbations, including temperature and atom number fluctuations, resulting in a good agreement between theoretical predictions and experimental results.
The importance of feedback control is being increasingly appreciated in quantum physics and applications. This paper describes the use of optimal control methods in the design of quantum feedback control systems, and in particular the paper formulates and solves a risk-sensitive optimal control problem. The resulting risk-sensitive optimal control is given in terms of a new unnormalized conditional state, whose dynamics include the cost function used to specify the performance objective. The risk-sensitive conditional dynamic equation describes the evolution of our {em knowledge} of the quantum system tempered by our {em purpose} for the controlled quantum system. Robustness properties of risk-sensitive controllers are discussed, and an example is provided.
Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
We study time-optimal protocols for controlling quantum systems which show several avoided level crossings in their energy spectrum. The structure of the spectrum allows us to generate a robust guess which is time-optimal at each crossing. We correct the field applying optimal control techniques in order to find the minimal evolution or quantum speed limit (QSL) time. We investigate its dependence as a function of the system parameters and show that it gets proportionally smaller to the well-known two-level case as the dimension of the system increases. Working at the QSL, we study the control fields derived from the optimization procedure, and show that they present a very simple shape, which can be described by a few parameters. Based on this result, we propose a simple expression for the control field, and show that the full time-evolution of the control problem can be analytically solved.
Optimal control theory is a powerful tool for solving control problems in quantum mechanics, ranging from the control of chemical reactions to the implementation of gates in a quantum computer. Gradient-based optimization methods are able to find high fidelity controls, but require considerable numerical effort and often yield highly complex solutions. We propose here to employ a two-stage optimization scheme to significantly speed up convergence and achieve simpler controls. The control is initially parametrized using only a few free parameters, such that optimization in this pruned search space can be performed with a simplex method. The result, considered now simply as an arbitrary function on a time grid, is the starting point for further optimization with a gradient-based method that can quickly converge to high fidelities. We illustrate the success of this hybrid technique by optimizing a holonomic phasegate for two superconducting transmon qubits coupled with a shared transmission line resonator, showing that a combination of Nelder-Mead simplex and Krotovs method yields considerably better results than either one of the two methods alone.
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