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arXiv:2101.03387 · Entropy

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

Qi Zhang, Xi Chen, David Guéry-Odelin

Published Jan 9, 2021• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/e23010084

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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.
Fast and robust quantum control protocols are often based on an idealized approximate description of the relevant quantum system.While this may provide a performance that is close to optimal, improvements can be made by incorporating elements of the full system representation.We propose a technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA).The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols.This correction can be easily calculated, and the resulting protocols are outside the class of STA schemes.We demonstrate the effectiveness of the method for three distinct cases: manipulation of an internal atomic state beyond the rotating-wave approximation, transport of a neutral atom in an optical Gaussian trap, and transport of two trapped ions in an anharmonic trap.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
Achieving fast, excitation-free quantum control is a vital challenge in modern quantum technologies. In many cases, shortcuts to adiabaticity enable fast adiabatic-like protocols, yet determining control parameters that satisfy practical constraints is often challenging in complex systems. Here, we combine an analytical shortcut to adiabaticity approach with several numerical optimization methods to boost the performance of the protocol. As a proof-of-principle for this hybrid approach, we study a particularly intricate control problem, the separation of two trapped ions. We show that this analytical-numerical approach, along with the physical insight gained through the variety of suboptimal solutions, leads to the exploration of new solutions in a complex landscape that yield improvements of up to 3 orders of magnitude. Moreover, this improvement comes with no additional cost from an experimental point of view.
A major barrier for the development of new quantum technologies is fast and robust methods for preparing and manipulating complex quantum states. To date preparation and manipulation of quantum systems has primarily been done using adiabatic processes. These adiabatic processes while robust have significant disadvantages such as their requiring long process times, a further drawback is that the system-environment interaction over these these long process times can lead to loss of coherence of the state of the system. A new area of study to achieve the robustness of adiabatic schemes but in time-scales much shorter is "Shortcuts to Adiabaticity" (STA). These STA techniques provide new methods for the manipulation of quantum systems that achieve high-fidelity state transfers in much shorter times. The aim of this thesis is to use STA and related methods for many particle systems. A method for manipulating a gas of fermions is developed using Pauli blocking and it’s robustness in the presence of temperature and different particle number investigated. A novel method for trapping and cooling particles using atom-diode and reflecting atomic mirror is investigated, both the classical and quantum cases are simulated. A method for transporting atoms and condensates across an optical lattice using invariant based inverse engineering is developed. Finally we look at non-hermitian potentials and design particular potentials that result in desirable asymmetries in the transmission and reflection of incident particles.