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physica status solidi (b)

Quantum State Transfer via Multi‐Passage Landau–Zener–Stückelberg Interferometry in a Three‐Qubit System

Zhiyuan Li, Danyu Li, Mengmeng Li, Xiaopei Yang, Shuqing Song, Zhikun Han, Zhen Yang, Ji Chu, Xinsheng Tan, Dong Lan, Haifeng Yu, Yang Yu

Published Sep 28, 2019• 5 citations
Publisher

Abstract

In quantum information processing, it is necessary to transfer quantum state between different systems. Herein, a scheme to transfer quantum state using multi‐passage Landau–Zener–Stückelberg interferometry in three superconducting qubits is proposed. A periodic triangle waveform quickly drives the system across the energy level anticrossing multiple times, inducing multiphoton Rabi oscillations. Using the 0‐photon Rabi oscillations, the dynamical quantum state transfer with probability close to 100% is realized. The fidelity of the state transfer is insensitive to local distortion of the driving waveform. This scheme can be extended to a system where multiple qubits are coupled to a frequency‐tunable qubit, as a quantum medium. It provides a useful tool for scalable quantum computing.

DOI
10.1002/pssb.201900459

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In quantum information processing, it is necessary to transfer quantum state between different systems. Herein, a scheme to transfer quantum state using multi‐passage Landau–Zener–Stückelberg interferometry in three superconducting qubits is proposed. A periodic triangle waveform quickly drives the system across the energy level anticrossing multiple times, inducing multiphoton Rabi oscillations. Using the 0‐photon Rabi oscillations, the dynamical quantum state transfer with probability close to 100% is realized. The fidelity of the state transfer is insensitive to local distortion of the driving waveform. This scheme can be extended to a system where multiple qubits are coupled to a frequency‐tunable qubit, as a quantum medium. It provides a useful tool for scalable quantum computing.
Schr\"odinger-cat states are useful for many applications, ranging from quantum-information processing to high-precision measurements. In this paper we propose a method for creating such cat states, based on photon-assisted Landau-Zener-St\"uckelberg interferometry in a hybrid system consisting of a qubit coupled to a photon cavity. We show that by initializing the qubit in one of its basis states, performing three consecutive sweeps of the qubit energy splitting across the 1-photon resonance, and finally projecting the qubit to the same basis state, the parity of the photon field can be purified to very high degree; when the initial photon state is a coherent state, the final state will then be very close to a Schr\"odinger-cat state. We present numerical simulations that confirm that our protocol could work with high fidelity ($\ensuremath{\sim}0.99$) for coherent states of reasonable size (${|\ensuremath{\alpha}|}^{2}\ensuremath{\sim}10$). Furthermore, we suggest that our protocol can also be used to transfer quantum information between the qubit and a superposition of orthogonal cat states in the cavity.
ABSTRACT Efficient and robust quantum state transfer between distinct optical modes is a cornerstone for on‐chip quantum networks and integrated quantum information processing. Here, we propose a protocol for fast photon transfer in a three‐mode system consisting of two optical cavities and an intermediate bosonic mode that is subjected to a periodic frequency modulation. In contrast to conventional adiabatic methods that require time‐varying coupling strengths, our scheme only modulates the frequency of the intermediate mode, significantly reducing experimental complexity. By mapping the dynamics onto a Landau–Zener–Stückelberg–Majorana (LZSM) interference model, we show that the bright normal mode accumulates a phase, enabling complete photon transfer from one cavity to the other. We systematically analyze the weak‐, strong‐, and intermediate‐driving regimes and demonstrate that the intermediate regime yields both high speed and prolonged target‐mode occupation, making the transfer resilient to timing errors. The protocol naturally extends to multi‐photon Fock states. Furthermore, we map the model onto a practical cavity optomechanical system with a mechanical oscillator as the intermediate mode, where numerical simulations based on realistic parameters confirm a transfer fidelity superior to recent two‐photon LZSM schemes. Our results provide a practical route toward fast, low‐complexity photon transfers in integrated optomechanical and microcavity systems.
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.
The quantum gate is the foundation of quantum computation and simulation in superconducting circuits. In recent years, quantum systems with three energy levels have attracted much attention. Therefore, it is essential to study the protocol of the quantum‐state transfer in qutrits. Herein, the all‐microwave schemes are studied to realize the state transfer and quantum gates. First, the ∣fg>–∣ge> transition is designed in a superconducting circuit with a relatively large coupling. We measured the Stark shift in cases where the experimental parameters did not satisfy the dispersive condition. Then, by carefully calibrating the pulse parameters, the regular Rabi oscillation and the state transfer are realized between the second excited state of two qubits via stimulated Raman adiabatic passage.
We study the dynamic behavior of a quantum two-level system with periodically varying parameters by solving numerically the master equation for the density matrix. Two limiting cases are considered: multiphoton Rabi oscillations and Landau–Zener transitions. The approach is applied to the description of the dynamics of superconducting qubits. In particular, the case of the interferometer-type charge qubit with periodically varying parameters (gate voltage or magnetic flux) is investigated. The time-averaged energy level populations are calculated as functions of the qubit’s control parameters.
In this study, Landau–Zener–Stückelberg–Majorana (LZSM) dynamics of tunneling transmon quantum bits (qubits) and related interference effects (interferometry) in symmetrical Josephson junctions (JJs) are theoretically investigated. Accordingly, the deviation of the driving parameters from the symmetry point and the transmon frequency are introduced, leading to fluctuations of a superconducting gap that limit the computational power of state-of-the-art transmon qubits and micro-processors. Indeed, the theoretical approach is carried withing the framework of the dynamic matrix approach (DMA) and numerical experiment measurements are reported after both single and double passages through a complexity of the transmon qubit polarization energy . Therefore, we derive generalized analytical expressions of LZSM quantum tunneling probabilities (QTP) and energy eigenvalues for multiple passages processes, which allow us to efficiently establish the transmon frequency and determine the driving parameters. Our theoretical results seem relevant for the interpretation of several LZSM interferometry mechanisms in the modulation of superconducting gap through different transmon qubit spectroscopy experiments in which tunable LZSM transitions and quantum interference patterns are demonstrated by the use of universal nonadiabatic control to implement quantum emulations. Additionally, this mapping enables the investigation of JJ effects through the identification of the corresponding modulated topological phases accumulated during the LZSM transitions, which offer new opportunities to coherently manipulate qubit states and address the energy transfer of transmon qubits on the one hand. On the other hand, it suggests possibilities to reduce sensitivity and to suspected sources of imperfection from different superconducting qubit architectures, particularly in the context of materials optimization strategies that dig out nontrivial phenomena possessing powerful quantum interferometer functionality with realistic quantum controls of tunneling transmon qubit states.