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arXiv:1504.03055 · Physical Review A

Manipulating the Majorana qubit with Landau-Zener-Stückelberg interference

Wenchao Huang, Qifeng Liang, Dao‐Xin Yao, Zhi Wang

Published Jul 8, 2015• 13 citations
arXivHTMLPDF

Abstract

Constructing a universal operation scheme for Majorana qubits remains a central issue for the topological quantum computation. We study the Landau-Zener-St\"uckelberg interference in a Majorana qubit and show that this interference can be used to achieve controllable operations. The Majorana qubit consists of an rf superconducting quantum interference device (SQUID) with a topological nanowire Josephson junction which hosts Majorana bound states. In the SQUID, a magnetic flux pulse can drive the quantum evolution of the Majorana qubit. The qubit experiences two Landau-Zener transitions when the amplitude of the pulse is tuned around the superconducting flux quanta $h/2e$. The Landau-Zener-St\"uckelberg interference between the two transitions rotates the Majorana qubit, with the angle controlled by the time scale of the pulse. This rotation operation implements a high-speed single-qubit gate on the Majorana qubit, which is a necessary ingredient for the topological quantum computation.

DOI
10.1103/physreva.92.012308

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Constructing a universal operation scheme for Majorana qubits remains a central issue for the topological quantum computation. We study the Landau-Zener-St"uckelberg interference in a Majorana qubit and show that this interference can be used to achieve controllable operations. The Majorana qubit consists of an rf superconducting quantum interference device (SQUID) with a topological nanowire Josephson junction which hosts Majorana bound states. In the SQUID, a magnetic flux pulse can drive the quantum evolution of the Majorana qubit. The qubit experiences two Landau-Zener transitions when the amplitude of the pulse is tuned around the superconducting flux quanta h/2eh/2eh/2e. The Landau-Zener-St"uckelberg interference between the two transitions rotates the Majorana qubit, with the angle controlled by the time scale of the pulse. This rotation operation implements a high-speed single-qubit gate on the Majorana qubit, which is a necessary ingredient for the topological quantum computation.
Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.
A radio frequency (rf) superconducting quantum interference device (SQUID) is a macroscopic quantum object consisting of a superconducting loop interrupted by a Josephson junction. Superconducting phase quantum bits (qubits) based on rf SQUIDs have been proven to be one of the most promising candidates for building a quantum computer. They exploit the unique resources of quantum superposition and entanglement and are exponentially faster than classical computers in solving certain problems, such as factoring. Compared to other approaches to quantum computing, superconducting phase qubits allow stronger and more flexible inter-qubit coupling and thus are easier to scale up. However, phase qubits couple to the environment and are subject to considerable decoherence. The resulting coherence time (also called decoherence time) is on the order of 100 ns, about two orders of magnitude shorter than that required for fault-tolerant quantum computing. One possible solution is to develop faster quantum gates in phase qubits. In this dissertation, coherent manipulation of multi-partite quantum states via Landau-Zener (LZ) transitions was investigated in a phase qubit, which was coupled to two microscopic two-level systems (TLSs) embedded in the tunnel barrier of the Josephson junction. The qubit chip was measured at temperatures below 30 mK in an ultra-low noise environment with excellent electrical and magnetic filtering and shielding. All parameters of the phase qubit were calibrated independently. The phase qubit's decoherence times have been carefully measured as well. Fast and precise coherent control of the tripartite quantum states has been successfully demonstrated by the observation of the Landau-Zener-Stückelberg (LZS) interference in the coupled qubit-TLS system. Furthermore, it is shown that utilizing LZ transitions to create multi-partite entangled states, such as the W state, is significantly more efficient than conventional methods which require a sequence of single-qubit and two-qubit gates. Hence, coherent manipulation of multi-partite quantum states via LZ transitions is a promising basis for a new family of fast multi-qubit quantum gates.
We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"uckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"uckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.
Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.
A basic requirement for quantum information processing is the ability to universally control the state of a single qubit on timescales much shorter than the coherence time. Although ultrafast optical control of a single spin has been achieved in quantum dots, scaling up such methods remains a challenge. Here we demonstrate complete control of the quantum-dot charge qubit on the picosecond scale [corrected], orders of magnitude faster than the previously measured electrically controlled charge- or spin-based qubits. We observe tunable qubit dynamics in a charge-stability diagram, in a time domain, and in a pulse amplitude space of the driven pulse. The observations are well described by Landau-Zener-Stückelberg interference. These results establish the feasibility of a full set of all-electrical single-qubit operations. Although our experiment is carried out in a solid-state architecture, the technique is independent of the physical encoding of the quantum information and has the potential for wider applications.
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].