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arXiv:2310.17932 · Physical Review Research

Alternative fast quantum logic gates using nonadiabatic Landau-Zener-Stückelberg-Majorana transitions

A. I. Ryzhov, O. V. Ivakhnenko, Sergey N Shevchenko, M. Fernando González-Zalba, Franco Nori

Published Sep 26, 2024• 15 citations
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Abstract

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

DOI
10.1103/physrevresearch.6.033340

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•Jan 1, 2020•34 citations
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
We investigate an analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM) in order to implement the QSP algorithm with fast quantum logic gates. QSP is an algorithmic technique that uses single-qubit dynamics to perform a polynomial function transformation. The adiabatic-impulse model effectively describes the evolution of a two-level quantum system under a strong external driving field. We can map parameters from QSP to the AIM to implement a QSP-like evolution with nonadiabatic, high-amplitude external drives. By choosing the AIM driving parameters that control the nonadiabatic transition parameters (such as driving amplitude A , frequency ω , and signal timing), one can achieve polynomial approximations and increase robustness in quantum circuits. The analogy between QSP and AIM presented here can be useful as a way to directly implement the QSP algorithmic technique on quantum systems and show the benefits from fast Landau-Zener-Stückelberg-Majorana (LZSM) quantum logic gates in comparison with usual resonance driving gates in IBM-Q quantum processors.
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.
Fast quantum gates are of paramount importance for enabling efficient and error-resilient quantum computations. In the present work we analyze Landau-Zener-St\"uckelberg-Majorana (LZSM) strong driving protocols, tailored to implement fast gates with particular emphasis on small-gap qubits. We derive analytical equations to determine the specific set of driving parameters for the implementation of single-qubit and two-qubit gates employing single-period sinusoidal pulses. Our approach circumvents the need to scan experimentally a wide range of parameters and instead it allows to concentrate on fine-tuning the device near the analytically predicted values. We analyze the dependence of relaxation and decoherence on the amplitude and frequency of the pulses, obtaining the optimal regime of driving parameters to mitigate the effects of the environment. Our study focus on the single-qubit ${X}_{\frac{\ensuremath{\pi}}{2}}, {Y}_{\frac{\ensuremath{\pi}}{2}}$ and identity gates. Also, we propose the bSWAP\sqrt{\mathrm{bSWAP}}bSWAP​ as the simplest two-qubit gate attainable through a robust LZSM driving protocol.
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].
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.
© 2020 authors. Published by the American Physical Society. Resonant transverse driving of a two-level system as viewed in the rotating frame couples two degenerate states at the Rabi frequency, an equivalence that emerges in quantum mechanics. While successful at controlling natural and artificial quantum systems, certain limitations may arise (e.g., the achievable gate speed) due to nonidealities like the counterrotating term. We introduce a superconducting composite qubit (CQB), formed from two capacitively coupled transmon qubits, which features a small avoided crossing - smaller than the environmental temperature - between two energy levels. We control this low-frequency CQB using solely baseband pulses, nonadiabatic transitions, and coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit operations with Clifford fidelities exceeding 99.7%. We also perform coupled qubit operations between two low-frequency CQBs. This work demonstrates that universal nonadiabatic control of low-frequency qubits is feasible using solely baseband pulses.