Robust quantum memory via quantum control

2001 OSA Technical Digest Series (Optica Publishing Group, 2001), paper PA2

Robustness of Energy Landscape Control to Dephasing

As shown in previous work, in some cases closed quantum systems exhibit a non-conventional trade-off in performance and robustness in the sense that controllers with the highest fidelity can also provide the best robustness to parameter uncertainty. As the dephasing induced by the interaction of the system with the environment guides the evolution to a more classically mixed state, it is worth investigating what effect the introduction of dephasing has on the relationship between performance and robustness. In this paper we analyze the robustness of the fidelity error, as measured by the logarithmic sensitivity function, to dephasing processes. We show that introduction of dephasing as a perturbation to the nominal unitary dynamics requires a modification of the log-sensitivity formulation used to measure robustness about an uncertain parameter with non-zero nominal value used in previous work. We consider controllers optimized for a number of target objectives ranging from fidelity under coherent evolution to fidelity under dephasing dynamics to determine the extent to which optimizing for a specific regime has desirable effects in terms of robustness. Our analysis is based on two independent computations of the log-sensitivity: a statistical Monte Carlo approach and an analytic calculation. We show that despite the different log sensitivity calculations employed in this study, both demonstrate that the log-sensitivity of the fidelity error to dephasing results in a conventional trade-off between performance and robustness.Comment: 11 pages, four figures, and three table

Sample-efficient Model-based Reinforcement Learning for Quantum Control

We propose a model-based reinforcement learning (RL) approach for noisy time-dependent gate optimization with improved sample complexity over model-free RL. Sample complexity is the number of controller interactions with the physical system. Leveraging an inductive bias, inspired by recent advances in neural ordinary differential equations (ODEs), we use an auto-differentiable ODE parametrised by a learnable Hamiltonian ansatz to represent the model approximating the environment whose time-dependent part, including the control, is fully known. Control alongside Hamiltonian learning of continuous time-independent parameters is addressed through interactions with the system. We demonstrate an order of magnitude advantage in the sample complexity of our method over standard model-free RL in preparing some standard unitary gates with closed and open system dynamics, in realistic numerical experiments incorporating single shot measurements, arbitrary Hilbert space truncations and uncertainty in Hamiltonian parameters. Also, the learned Hamiltonian can be leveraged by existing control methods like GRAPE for further gradient-based optimization with the controllers found by RL as initializations. Our algorithm that we apply on nitrogen vacancy (NV) centers and transmons in this paper is well suited for controlling partially characterised one and two qubit systems.Comment: 14+6 pages, 6+4 figures, comments welcome

Quantification of edited magnetic resonance spectroscopy: a comparative phantom based study of analysis methods

A calibrated series of MRS phantoms is used to compare the performance of common spectroscopy analysis tools in the quantification of GABA-edited spectroscopy data. Varied GABA concentration, and simulated spectra provide a ground truth with which to compare

Robustness of energy landscape controllers for spin rings under coherent excitation transport

The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control and generates results in contradiction to the expectations of classical control theory. This paper examines the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the robustness measure, drawing on the classical control analog of the sensitivity of the tracking error. Our analysis shows that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window T ± Δ/2

Statistically characterizing robustness and fidelity of quantum controls and quantum control algorithms

Robustness of quantum operations or controls is important to build reliable quantum devices. The robustness-infidelity measure (RIM_p) is introduced to statistically quantify in a single measure the robustness and fidelity of a controller as the p-th order Wasserstein distance between the fidelity distribution of the controller under any uncertainty and an ideal fidelity distribution. The RIM_p is the p-th root of the p-th raw moment of the infidelity distribution. Using a metrization argument, we justify why RIM_1 (the average infidelity) is a good practical robustness measure. Based on the RIM_p, an algorithmic robustness-infidelity measure (ARIM) is developed to quantify the expected robustness and fidelity of controllers found by a control algorithm. The utility of the RIM and ARIM is demonstrated on energy landscape controllers of spin-1/2 networks subject to Hamiltonian uncertainty. The robustness and fidelity of individual controllers as well as the expected robustness and fidelity of controllers found by different popular quantum control algorithms are characterized. For algorithm comparisons, stochastic and non-stochastic optimization objectives are considered. Although high fidelity and robustness are often conflicting objectives, some high-fidelity, robust controllers can usually be found, irrespective of the choice of the quantum control algorithm. However, for noisy or stochastic optimization objectives, adaptive sequential decision-making approaches, such as reinforcement learning, have a cost advantage compared to standard control algorithms and, in contrast, the high infidelities obtained are more consistent with high RIM values for low noise levels