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.
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.
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.
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.
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.
By driving a 3D transmon with microwave fields, we generate an effective avoided energy-level crossing. Then we chirp microwave frequency, which is equivalent to driving the system through the avoided energy-level crossing by sweeping the avoided crossing. A double-passage chirp produces Landau-Zener-Stückelberg-Majorana (LZSM) interference that agree well with the numerical results, especially with the initial state being an eigen-energy state in the center of an avoided level crossing. A time-resolved state tomography measurement is performed in the evolution of LZSM interference, showing an experimental evidence for the dynamical evolution of quantum state. Our method is fully applicable to other quantum systems that contain no intrinsic avoided level crossing, providing an alternative approach for quantum control and quantum simulation.
Since the pioneering works by Landau, Zener, Stückelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for manipulating a growing number of quantum systems. Here, we systematically study various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in Ref. [504].
We investigate the transfer between spin quantum bit (qubit) states and study the Landau–Zener–Stückelberg–Majorana (LZSM)-like dynamics of tunneling spin qubits in a multiband two-state magnetic quantum wire. Indeed, within the framework of an optical parabolic potential in a three-dimensional (3D) heterostructure quantum wire and under the influence of an external time-varying magnetic field, a model for a multiband two-state magnetic quantum wire is developed. Here, the external magnetic field is used to coherently manipulate and control spin qubit states. By driving the system through an avoided crossing, we consider the associated effective quantum two-level system (TLS) related to the spin qubit states in each band, driving by an external coherent magnetic field in which the related Hamiltonian is Hermitian, and which generally paves a way to LZSM interferometry. Thus, we establish the analytical expressions of the energy eigenvalues in each band and derive the analytical solution of the dynamical evolution of the tunneling probabilities of the associated TLS. Accordingly, nonadiabatic and adiabatic tunneling probabilities (survival and transition) are calculated for each band of the multiband TLS. In this respect, the nonadiabatic and adiabatic dynamical evolutions of the tunneling probabilities of spin qubit populations in the first four bands, with band quantum numbers n = 0, 1, 2 and 3 are analyzed. As a result, depending on the amplitude strength of the driven magnetic field and the magnitude of the driving frequency, we report two striking nonadiabatic and adiabatic scenarios in each band for both the diabatic and adiabatic states. In this context, driving the two states of each band of the multiband TLS related to the spin qubit states through an avoided level crossing can result in nontrivial and incoherent dynamics at certain phases, resulting to apparent inaccurate probabilities, especially in the case of strong driven magnetic field and high driving frequency.