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arXiv:2406.07433 · Journal of Physics B Atomic Molecular and Optical Physics

Shortcuts to adiabaticity designed via time-rescaling follow the same transitionless route

J. L. Montenegro Ferreira, Ângelo F. da Silva França, Alexandre Rosas, Bertúlio de Lima Bernardo

Published Jan 13, 2026• 1 citation
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Abstract

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.

DOI
10.1088/1361-6455/ae37b0

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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.
The promotion of efficient population inversion in single quantum systems is a useful tool in quantum information and quantum computation sciences, since it allows for the precise preparation of states and the construction of logical gates such as the Hadamard. In this work we present a protocol to accelerate the population inversion in three-level atomic systems, by using the time rescaling (TR) shortcut to adiabaticity to speed up the STIRAP (Stimulated Raman Adiabatic Passage) protocol. We also show that the TR method follows the same path as the reference protocol, meaning that, if the reference protocol is an adiabatic dynamics, the shortcut to adiabaticity obtained via the TR method is transitionless, similar to the one obtained from the Counterdiabatic method. This introduces simplifications in our evaluation. Finally, we discuss the fidelity and thermodynamic cost of the protocol.
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.
A shortcut to adiabaticity is concerned with the fast and robust manipulation of the dynamics of a quantum system which reproduces the effect of an adiabatic process. In this work, we use the time-rescaling method to study the problem of speeding up the population inversion of a two-level quantum system, and the fidelity of the fast dynamics versus systematic errors in the control parameters. This approach enables the generation of shortcuts from a prescribed slow dynamics by simply rescaling the time variable of the quantum evolution operator. It requires no knowledge of the eigenvalues and eigenstates of the Hamiltonian and, in principle, no additional coupling fields. From a quantum thermodynamic viewpoint, we also demonstrate that the main properties of the distribution of work required to drive the system along the shortcuts are unchanged with respect to the reference (slow) protocol.
A shortcut to adiabaticity is a recipe for generating adiabatic evolution at an arbitrary pace. Shortcuts have been developed for quantum, classical and (most recently) stochastic dynamics. A shortcut might involve a counterdiabatic (CD) Hamiltonian that causes a system to follow the adiabatic evolution at all times, or it might utilize a fast-forward (FF) potential, which returns the system to the adiabatic path at the end of the process. We develop a general framework for constructing shortcuts to adiabaticity from flow fields that describe the desired adiabatic evolution. Our approach encompasses quantum, classical and stochastic dynamics, and provides surprisingly compact expressions for both CD Hamiltonians and FF potentials. We illustrate our method with numerical simulations of a model system, and we compare our shortcuts with previously obtained results. We also consider the semiclassical connections between our quantum and classical shortcuts. Our method, like the FF approach developed by previous authors, is susceptible to singularities when applied to excited states of quantum systems; we propose a simple, intuitive criterion for determining whether these singularities will arise, for a given excited state.
In quantum information processing, the shortcut-to-adiabaticity (STA) protocol has been proposed to accelerate a system's adiabatic evolution by introducing an additional, counterdiabatic Hamiltonian. This protocol is particularly suitable for realizing the controlled-ZZZ ($C\phantom{\rule{0}{0ex}}Z$) gate, but a counterdiabatic Hamiltonian requires a variable, complex coupling of qubits. By introducing a representation transformation and a rescaling method, this work uses the STA protocol to obtain a high-fidelity $C\phantom{\rule{0}{0ex}}Z$ gate with two coupled transmon qubits. This method affords high flexibility in the evolution time and control waveform, and is expected to be directly useful in other quantum systems as well.
Abstract Robust quantum control is essential for the development of quantum computers, which rely on precise manipulation of qubits. One form of quantum control is stimulated Raman adiabatic passage (STIRAP), which ordinarily is a state transfer protocol but was extended by Kis and Renzoni (2002 Phys. Rev. A 65 032318) to perform qubit rotations. Shortcut methods to adiabaticity for STIRAP have been shown to speed up adiabatic processes, beyond the adiabatic criterion, with high fidelity. Here, we apply shortcut to adiabaticity methods to the STIRAP qubit rotation scheme to improve the performance of quantum logic gates. The scheme can be implemented via direct connections between ground states in a 4-level Λ system or effective connections in a 5-level Λ system with modified pulses that implement transitionless quantum driving via the addition of a counterdiabatic driving term. We show that the extended shortcut to adiabaticity method serves to improve the fidelity of qubit rotations in the diabatic regime.