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arXiv:2207.02246 · Physical Review Applied

Robust Control of Linear Systems and Shortcut to Adiabaticity Based on Superoscillations

Qi Zhang, Xi Chen, David Guéry-Odelin

Published Nov 17, 2022• 6 citations
arXivHTMLPDF

Abstract

With the advent of quantum technologies, control issues are becoming increasingly important. In this paper, we address control in phase space under a global constraint provided by a minimal energylike cost function and a local (in Fourier space) constraint resulting from a robustness criterion. The inverse-engineering Lagrangian formalism developed here generalizes the formalism commonly used to describe the superoscillation phenomenon. It is applied to both nondissipative and dissipative quantum mechanics, and extended to stochastic thermodynamics. Interestingly, our approach also allows one to improve sensing capabilities by appropriate control of the system.

DOI
10.1103/physrevapplied.18.054055

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With the advent of quantum technologies, control issues are becoming increasingly important. In this paper, we address control in phase space under a global constraint provided by a minimal energylike cost function and a local (in Fourier space) constraint resulting from a robustness criterion. The inverse-engineering Lagrangian formalism developed here generalizes the formalism commonly used to describe the superoscillation phenomenon. It is applied to both nondissipative and dissipative quantum mechanics, and extended to stochastic thermodynamics. Interestingly, our approach also allows one to improve sensing capabilities by appropriate control of the system.
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We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.
This paper surveys some recent results on the feedback control of quantum linear systems and the robustness properties of these systems. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). These systems can also be described in terms of a Hamiltonian operator H and a coupling operator L, which in the case of quantum linear systems have a specific quadratic and linear form respectively. Such systems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or approximated by linear QSDEs include interconnections of optical cavities, beam-splitters, phase-shifters, optical parametric amplifiers, optical squeezers, and cavity quantum electrodynamic systems. An important approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. The paper discusses recent results concerning the synthesis of coherent quantum controllers such as in coherent quantum H∞ control. Another important issue in the design of quantum feedback controllers is the robustness of the closed loop quantum system to perturbations in the quantum plant dynamics arising from perturbations in the system Hamiltonian H and the system coupling operator L. The paper discusses recent robust stability results for such perturbed quantum systems which take the form of a quantum small gain theorem and a quantum Popov stability criterion. These results are usefu
Shortcuts to adiabaticity (STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse-engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy (N-VVV) center. The microwave pulses to drive inversely engineered STA are obtained with space-curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of N-VVV system, and thus benefits quantum sensing and quantum computation based on the N-VVV platform.
Shortcuts to adiabaticity~(STA) enables fast and robust coherent control of quantum system, which has been well placed in quantum technologies. In particular, inverse engineering STA provides much more freedom for the optimization of shortcut, which alleviates the complexity for experimental realization. Here, we implement a STA technique, known as invariant-based inverse engineering, to speed up the adiabatic control of the electron triplet ground state of a single nitrogen-vacancy~(NV) center. The microwave pulses to drive inversely engineered STA are obtained with space curve quantum control, where the evolution of spin transition is mapped to a three-dimensional closed space curve and the design of shortcut is obtained by optimization over the space curve. We demonstrate the fast and high-fidelity drive of dipole-forbidden transition between two spin sublevels of the ground state. Moreover, we demonstrate the robustness of the spin transition by introducing the detuning of driving microwave field. The acceleration and robustness is further confirmed by the comparison with two traditional Raman control schemes. Our results suggest invariant-based inverse engineering is powerful for fast and robust manipulation of NV system, and thus benefits quantum sensing and quantum computation based on the NV platform.