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arXiv:2607.16829

Shortcuts to adiabaticity in five-level systems using counter-diabatic driving and time-rescaling optimization

Jiahui Zhang, Wenyuan Wang, Fuquan Dou

quant-phSubmitted Jul 18, 2026• Announced Jul 21, 2026• 0 citations
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Abstract

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.

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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.
Shortcuts to adiabaticity in various quantum systems have attracted much attention with their wide applications in quantum information processing and quantum control. In this paper, we concentrate on a stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counterdiabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counterdiabatic driving along with the unitary transformation and eventually modify the pump and Stokes pulses for achieving fast and high-fidelity population transfer. The required laser intensity and stability against parameter variation are further discussed, to demonstrate the advantage of shortcuts to adiabaticity.
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.
The shortcut to adiabaticity (STA) is a powerful technique to speed up population transfer via quantum coherent control. This paper demonstrates that STA provides a fast, robust, and efficient population transfer compared to the stimulated Raman adiabatic passage. In the ideal situation of a closed system, STA is insensitive to the detunings and Rabi frequencies, and the undesired diabatic transitions could be eliminated by the auxiliary pulses, so the complete population transfer from the initial state to the target state in the designed adiabatic passage can be rapidly achieved against the inevitable amplitude noises of the interactions and systematic errors. When we consider the situation including the environment noises, spontaneous emission from the intermediate state $|2\ensuremath{\rangle}$ in STA can be sufficiently ignored in the cases of the dark-state evolution and quantum overdamping, since the state $|2\ensuremath{\rangle}$ is thoroughly separated from the three-state system. Moreover, the diabatic transitions induced by the spontaneous emission are also sufficiently suppressed in STA.
Abstract The multistate stimulated Raman adiabatic passage (STIRAP) is an efficient technique to achieve a selective and accurate population transfer in a chainwise-linked system. However, their efficiency is imperfect due to the nonadiabatic losses from the long runtime of the adiabatic evolution. Here, we focus on realizing a perfect and robust coherent control of the quantum states with optimal shortcut to adiabaticity in a realistic five-state hybrid quantum system. In particular, the optimal shortcut field requires minimal additional coupling (only one coupling strength) to accelerate the adiabatic evolution in this five-state system. Compared to the original STIRAP, the optimal shortcut shows the ultra-high fidelity of quantum state manipulations even though the control parameters of the Hamiltonians are changed in different ways. Furthermore, we study the efficiency of the optimal shortcut field technique in the presence of various experimental errors, such as systematic error, Rabi frequency error, and coupling strength error, and it features a broad range of high efficiencies above 99.9%, showing its robustness against the above errors. The results might shed insight on the further applications of shortcuts to adiabaticity on robust quantum information processing in multi-level quantum systems.
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.