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Chinese Physics Letters

Superadiabatic Multiphoton Landau–Zener–Stückelberg–Majorana Effect in a Transmon Qudit

Pei-Yao Song, Jin‐Lei Wu, Shi‐Lei Su

Published Mar 3, 2026• 1 citation
Publisher

Abstract

Abstract The recently observed two-photon Landau–Zener–Stückelberg–Majorana (LZSM) effect in superconducting circuits [ Phys. Rev. Lett. 134 060602 (2025) ] has provided a robust pathway for high-fidelity population transfer in qudit systems, but its adiabatic nature necessitates long operation times, which are vulnerable to decoherence. In this paper, we present a practical acceleration scheme based on a superadiabatic (SUAD) framework that overcomes these fundamental limitations. Our approach is tailored to a multiphoton LZSM process. By constructing modified pulse envelopes for the existing drive field without introducing auxiliary counterdiabatic controls, we achieve accelerated high-fidelity state transfer from the ground state to the target excited state. For the two-photon case, our protocol reduces the operation time by more than four times compared with the adiabatic reference, while maintaining a fidelity of 0.998. We further generalize this to the three-photon regime, demonstrating a speedup factor exceeding three. Our SUAD LZSM scheme exhibits superior resilience to decoherence, offering a ready-to-implement solution for the fast and reliable control of multilevel quantum hardware.

DOI
10.1088/0256-307x/43/4/040601

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A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with nonresonant driving and the alternation of adiabatic evolution and nonadiabatic transitions. Compared to Rabi oscillations, the main differences are a nonresonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing the gate speed. We define the parameters of the external driving required for implementing a specific quantum logic gate using the adiabatic-impulse model. In particular, we demonstrate the implementations of single-qubit X, Y, Hadamard gates, and two-qubit i and gates using the LZSM transitions. The considered LZSM approach for implementing arbitrary quantum logic gates can be applied to a large variety of multilevel quantum systems and external driving. Published by the American Physical Society 2024

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Abstract The recently observed two-photon Landau–Zener–Stückelberg–Majorana (LZSM) effect in superconducting circuits [ Phys. Rev. Lett. 134 060602 (2025) ] has provided a robust pathway for high-fidelity population transfer in qudit systems, but its adiabatic nature necessitates long operation times, which are vulnerable to decoherence. In this paper, we present a practical acceleration scheme based on a superadiabatic (SUAD) framework that overcomes these fundamental limitations. Our approach is tailored to a multiphoton LZSM process. By constructing modified pulse envelopes for the existing drive field without introducing auxiliary counterdiabatic controls, we achieve accelerated high-fidelity state transfer from the ground state to the target excited state. For the two-photon case, our protocol reduces the operation time by more than four times compared with the adiabatic reference, while maintaining a fidelity of 0.998. We further generalize this to the three-photon regime, demonstrating a speedup factor exceeding three. Our SUAD LZSM scheme exhibits superior resilience to decoherence, offering a ready-to-implement solution for the fast and reliable control of multilevel quantum hardware.
ABSTRACT We propose and theoretically demonstrate a tailored shortcut to adiabaticity for accelerating the two‐photon Landau‐Zener‐Stückelberg‐Majorana (LZSM) transition in a superconducting transmon qutrit. Unlike conventional single‐photon LZSM processes, the two‐photon variant involves a virtual intermediate state and arises from a constrained three‐level dynamics with weak anharmonicity, leading to a nonlinear dependence of the effective Rabi coupling on the drive amplitude and stringent requirements on frequency modulation. Using the Lewis‐Riesenfeld invariant method, we construct an exact dynamical invariant for implementing a two‐photon LZSM transition with experimentally feasible, time‐dependent amplitude, and frequency modulation profiles that steer the system along an invariant eigenstate. Our protocol achieves high‐fidelity population transfer from the ground state to the second excited state in just ns, over faster than the reference adiabatic scheme. Crucially, the shortcut preserves the inherent robustness of the LZSM process against drive amplitude errors and exhibits enhanced resilience to decoherence due to the shortened operation time. This work provides a general and practical framework for accelerating higher‐order quantum transitions in multilevel systems, with direct relevance to ultrafast qudit control and scalable quantum information processing.
Harnessing second-order processes enables new control schemes in quantum dynamics. We show that the Landau-Zener-Stückelberg-Majorana (LZSM) transition can be generalized to a virtual-state process in a three-level system, employing a phase modulated drive whereby two photons excite the system from the first to the third level while avoiding the second one. We implement experimentally this process in a transmon, achieving 98% population transfer. We predict and observe the doubling of LZSM velocity. Furthermore, we demonstrate robustness to amplitude and frequency offsets, made possible by the nearly exact cancellation of the two-photon ac Stark shift due to the presence of the fourth state.
In recent decades, a lot of effort has been seen to realize and control a large-scale quantum computer. Among the most promising architectures for such a system is that of superconducting circuits. However, a significant challenge with these qubits is the drifts in system parameters. Therefore, controlling thousands or more qubits - which are needed to perform practical applications - becomes increasingly difficult and various control schemes and workarounds are needed to vanquish such obstacles. One approach to cope with the complexity of the system size is to increase the information held per quantum system by introducing an additional state and thereby reduce the number of qubits. Therefore, in this work, we explore a robust population transfer, from the ground to the second excited state, on the first three levels of a superconducting transmon. For a transmon, such a transition cannot occur by single photon absorption. However, because of a second-order process, two-photon transitions from the ground state to the second excited state are possible for a drive at the 02-transition frequency. In existing protocols that drive this population transfer, such as the Raman process and (sa)STIRAP, a common problem is the sensitivity to offsets in frequency and amplitude of the drive pulses. Therefore, in search of a method that realizes such a transfer and is robust to some offsets we took inspiration from \cite{Mppr} and approached the problem through a Landau-Zener process. The Landau-Zener process in this work was a result of modulating the frequency of a one-tone drive around the 02-transition frequency that interchanged the first and third energy levels while avoiding the intermediate level. With this method, the three-level quantum system (approximately) follows the first eigenstate of the Hamiltonian adiabatically to the second excited state. This method showed considerable robustness to both offsets in frequency and amplitude and was eventually tested experimentally on a superconducting transmon. The results showed great agreement with the theory and demonstrates a method that is robust and simple enough to be realized on the majority of control hardware.
Abstract In many quantum technologies adiabatic processes are used for coherent quantum state operations, offering inherent robustness to errors in the control parameters. The main limitation is the long operation time resulting from the requirement of adiabaticity. The superadiabatic method allows for faster operation, by applying counterdiabatic driving that corrects for excitations resulting from the violation of the adiabatic condition. In this article we show how to construct the counterdiabatic Hamiltonian in a system with forbidden transitions by using two-photon processes and how to correct for the resulting time-dependent ac-Stark shifts in order to enable population transfer with unit fidelity. We further demonstrate that superadiabatic stimulated Raman passage can realize a robust unitary NOT-gate between the ground state and the second excited state of a three-level system. The results can be readily applied to a three-level transmon with the ladder energy level structure.
Quantum gates based on resonant Rabi oscillations are inherently slow for small-frequency qubits. They are also prone to errors due to counter-rotating terms. However, when the anharmonicity is sufficiently high, as in the fluxonium architecture, alternative manipulation protocols can outperform standard resonant driving. In this work, we implement fast, high-fidelity quantum gates based on a one-period Landau-Zener-Stückelberg-Majorana (LZSM) driving protocol. We derive analytical expressions that simplify the exploration of the parameter space while accounting for the multi-level structure of the circuit. Furthermore, we analyze the role of leakage, discussing strategies to mitigate it and identifying regimes in which it becomes the dominant source of error. Finally, to evaluate the impact of dissipation on gate fidelity, we develop a robust formalism suitable for analyzing the open-system performance of quantum gates in the strong driving regime.
A conventional realization of quantum logic gates and control is based on resonant Rabi oscillations of the occupation probability of the system. This approach has certain limitations and complications, like counter-rotating terms. We study an alternative paradigm for implementing quantum logic gates based on Landau-Zener-Stückelberg-Majorana (LZSM) interferometry with nonresonant driving and the alternation of adiabatic evolution and nonadiabatic transitions. Compared to Rabi oscillations, the main differences are a nonresonant driving frequency and a small number of periods in the external driving. We explore the dynamics of a multilevel quantum system under LZSM drives and optimize the parameters for increasing the gate speed. We define the parameters of the external driving required for implementing a specific quantum logic gate using the adiabatic-impulse model. In particular, we demonstrate the implementations of single-qubit X, Y, Hadamard gates, and two-qubit i and gates using the LZSM transitions. The considered LZSM approach for implementing arbitrary quantum logic gates can be applied to a large variety of multilevel quantum systems and external driving. Published by the American Physical Society 2024