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arXiv:2507.08439 · Physical Review A

Reversing adiabatic state preparation in few-level quantum systems

Leonardo Romanato, Najmeh Eshaqi-Sani, Luca Lepori, Teodora Kirova, E. Arimondo, Sandro Wimberger

Published Nov 12, 2025• 3 citations
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Abstract

We present a detailed study of an adiabatic state preparation in an effective three-level quantum system. States can be prepared with high speed and fidelity by adding a counterdiabatic quantum control protocol. As a second step, we invert the preparation protocol to get back to the initial state. This describes an overall cyclic evolution in state space. Using counterdiabatic terms, the resulting composed fast evolution can be repeated many times. We then analyze the control of Berry's phase along the adiabatic cyclic path and show that Berry's phase can act as a sensitive detector of nonperfect state transfer.

DOI
10.1103/pst6-r584

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We present a detailed study of an adiabatic state preparation in an effective three-level quantum system. States can be prepared with high speed and fidelity by adding a counterdiabatic quantum control protocol. As a second step, we invert the preparation protocol to get back to the initial state. This describes an overall cyclic evolution in state space. Using counterdiabatic terms, the resulting composed fast evolution can be repeated many times. We then analyze the control of Berry's phase along the adiabatic cyclic path and show that Berry's phase can act as a sensitive detector of nonperfect state transfer.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
We propose a scheme to speed up adiabatic passage by using Lyapunov control theory. This is a good choice to solve the problem that may emerge in Berry's transitionless quantum driving [M. V. Berry, J. Phys. A 42, 365303 (2009)]. That is, the extra couplings in the counterdiabatic driving Hamiltonian can be avoided by choosing the available control Hamiltonian in an actual physical system. As examples, we shorten the evolution time of adiabatic population transfer in a three-level system and the entanglement generation in a cavity quantum electrodynamics system. Moreover, the occupation of an intermediate state can be sharply suppressed by properly choosing the control Hamiltonian in the three-level system. The scheme can also be generalized to a complex system where the exact expressions of adiabatic eigenstates are difficult to obtain.
We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at all times. The strategy is based on the introduction of an effective counterdiabatic scheme: a correcting Hamiltonian is constructed which approximatively cancels nonadiabatic effects, inducing an evolution tracking the adiabatic states closely. This can be absorbed into the initial Hamiltonian by adding a fast oscillation in the control parameters. We show that a consistent speedup can be achieved without requiring strong control Hamiltonians, using it both as a stand-alone shortcut to adiabaticity and as a weak correcting field. A number of examples are treated, dealing with quantum state transfer in avoided-crossing problems and entanglement creation.
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.
Local counterdiabatic driving (CD) provides a feasible approach for realizing approximate adiabatic or reversible processes like quantum state preparation using only local controls and without demanding excessively long protocol times. However, in many instances getting high accuracy of such CD protocols requires engineering very complicated new controls or pulse sequences. In this work, we describe a systematic method for altering the adiabatic path by adding extra local controls along which performance of local CD protocols is enhanced, both close to and far from the adiabatic limit. We also identify an iterative procedure to improve the performance of local counterdiabatic driving further without any knowledge of the quantum wave function. We then show that these methods provides dramatic improvement in the preparation of nontrivial Greenberger-Horne-Zeilinger ground states of several different spin systems with both short-range and long-range interactions.
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.