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Landau-Zener driven 02-övergång i en transmon krets

Björkman, Isak

Published Dec 13, 2022• 0 citations
OpenAlex

Abstract

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.

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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.
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 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.
Adiabatic manipulation of the quantum state is an essential tool in modern quantum information processing. Here, we demonstrate the speedup of the adiabatic population transfer in a three-level superconducting transmon circuit by suppressing the spurious nonadiabatic excitations with an additional two-photon microwave pulse. We apply this superadiabatic method to the stimulated Raman adiabatic passage, realizing fast and robust population transfer from the ground state to the second excited state of the quantum circuit.
The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering--enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic-adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level.
Quantum computers are a promising new technology that enables the use of quantum algorithms to solve certain problems faster than classical computers. An especially auspicious method for realizing such a device is using a superconducting circuit as the foundational computational unit of the quantum computer, the qubit. These serve as two-level systems allowing for the storage and manipulation of quantum information. For large-scale adoption, precise control of qubits via rapid driving pulses is essential in order to carry out desired operations known as quantum gates. In superconducting qubits, this is often achieved with an external electromagnetic field coupled to the qubit capacitively or inductively. In this case, to achieve faster pulses, the power of the driving field must be increased. This, however, leads to increased heating of the qubit, which in turn can lead to decoherence and the loss of quantum information. One proposed solution is the use of off-resonance driving of the qubit, which enables faster pulses with lower driving power when compared to resonance drive. It also allows for drive line attenuation at the qubit frequency, suppressing decay of the qubit’s energy into the drive line. Another challenge in the operation of the qubit is preventing excitation outside the two states used for computation, known as the computational subspace. In this thesis, we look at optimizing the drive pulse shape as a remedy to this problem in the context of resonance drive, as well as two off-resonant driving methods: subharmonic drive and two-frequency drive. In particular, we make use of the Derivative Removal by Adiabatic Gate (DRAG) method with different pulse shapes in order to attenuate the transition between the first and second excited states of the qubit. The results are obtained with numerical simulation for the transmon, which is a common superconducting qubit. The results show strong suppression of leakage outside the computational subspace using the DRAG method in resonance and two-frequency drive, while in subharmonic drive, no major advantage is gained. We find that in all cases, the edge profiles of driving pulses have major effects on the excitation of unwanted transitions, suggesting that pulse shape optimization is a viable method for improving quantum gate fidelity in all three driving regimes.