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arXiv:2211.02543

Shortcuts to Adiabaticity with Inherent Robustness and without Auxiliary Control

Yiyao Liu, Zhenyu Wang

Published Nov 4, 2022• 0 citations
arXivHTMLPDF

Abstract

Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applications of our theory, we demonstrate reduction of the effects of both dissipation and dephasing noise by a novel robust three-level control, as well as reliable and fast ground state evolution in an adiabatic quantum computing model. Our theory offers a new route to design robust and fast control methods for general quantum systems.

DOI
10.48550/arxiv.2211.02543

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Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applications of our theory, we demonstrate reduction of the effects of both dissipation and dephasing noise by a novel robust three-level control, as well as reliable and fast ground state evolution in an adiabatic quantum computing model. Our theory offers a new route to design robust and fast control methods for general quantum systems.
Abstract Time-rescaling (TR) has been recently proposed as a method to engineer fast processes, also known as shortcuts to adiabaticity (STA), which enables the coherent control of quantum systems beyond the adiabatic regime (Bernardo 2020 Phys. Rev. Res. 2 013133). In this work, we revisit the technique and show that the obtained fast dynamics are transitionless, similar to the ones designed via the famous counterdiabatic (CD) approach. However, contrary to the CD approach, the TR method has the advantage of providing the Hamiltonians that generate the fast processes without requiring information about the instantaneous eigenstates of a reference protocol, and the convenience that experimental implementations dismiss additional coupling fields when compared with the reference adiabatic protocol. Here, we also show that the time evolution of the STA found via TR relates to that of the reference adiabatic protocol by a simple reparametrization of time. To illustrate our findings, we studied the paradigmatic problem of speeding up the stimulated Raman adiabatic passage and found out that TR revealed quantum dynamics more robust to parameter variations than those provided by the CD technique. These results motivate the application of TR to the control of larger quantum systems.
Shortcuts to adiabaticity (STA) is a common protocol to realize high-fidelity and robust quantum control in various quantum systems. To date, STA has been widely applied in two- and three-level systems, whereas designing feasible strategies to achieve perfect quantum state engineering in multi-level systems still remains a challenging task. Here, we propose to use counterdiabatic (CD) driving and time-rescaling (TR) methods to construct multi-state stimulated Raman shortcut-to-adiabatic passage protocols for realizing robust and fast population transfer in chainwise-connected five-state systems. The first protocol is implemented by initially reducing the original five-state system to an equivalent two-state counterpart, and then designing the corresponding driving field by combining CD driving and unitary transformation. Further, we introduce the TR method to optimize the first protocol and thus offers an alternative solution. Numerical calculations show that both protocols can achieve complete population transfer and effectively suppress transient populations of all intermediate states. Compared with the first protocol, the optimized second exhibits better performance within a shorter evolution time.
Shortcut to adiabaticity (STA) is a speedway to produce the same final state that would result in an adiabatic, infinitely slow process. Two typical techniques to engineer STA are developed by either introducing auxiliary counterdiabatic fields or finding new Hamiltonians that own dynamical invariants to constraint the system into the adiabatic paths. In this paper, an efficient method is introduced to naturally cover the above two techniques with a unified Lie algebraic framework and neatly remove the design difficulties and loose assumptions in the two techniques. A general STA scheme for different potential expansions concisely achieves with the aid of squeezing transformations.
Abstract Realization of a large‐scale quantum computation relies on fast and high‐fidelity quantum control. Geometric quantum control is thought to be a promising candidate for quantum computation which consolidates the robustness against both random noise (through the global geometrical feature) and systematic errors (through adiabatic characteristic). The adiabatic process of geometric control can be accelerated through an auxiliary Hamiltonian in different scenarios by means of shortcuts to adiabaticity (STA). Especially, the auxiliary Hamiltonian can be absorbed into the original interacting configuration in most of the cases, which allows STA to coalesce with the Abelian or the non‐Abelian geometric control. As a consequence, geometric quantum control can have an enhanced robustness against decoherence after speeding up by STA. Here, the recent theoretical and experimental advances in geometric quantum computation based on STA are reviewed.
Multisqueezed states, also known as generalized squeezed states, are valuable quantum non-Gaussian resources, because they can feature nonclassical properties such as large phase-space Wigner negativities. In this paper, we introduce a shortcuts to adiabaticity (STA) method for the fast preparation of multisqueezed states. In contrast to previous STA methods, which rely on the use of counterdiabatic control to suppress unwanted nonadiabatic effects, our method simplifies the process and accelerates state preparation by selecting an appropriate sampling along a quantum evolution path. We demonstrate the high fidelity and fast preparation of multisqueezed states, as well as hybrid entangled states between a bosonic mode and a qubit.
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.