超導量子位元Xmon之優化控制

Optimal Control on Superconducting Xmon Qubits

廖允執(Yun-Chih Liao)

指導教授 ： 管希聖

國立臺灣大學/理學院/物理學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902941

摘要

量子計算是現今科學發展不可或缺的一環。為達到更快速之運算速度並處理複 雜度更高之研究議題，許多科學家開始著手研究量子電腦，量子位元即為量子 電腦之基本單元。常見製作材料有:超導體、半導體、離子井、光學晶格、電 子與光子等。本研究專注於由超導體打造之量子位元Xmon(其電路結構參考論文[1])，透過電腦模擬由此量子電路製成的單量子位元邏輯閘:反閘(not gate)與兩種雙量子位元邏輯閘:互換閘(swap gate)及受控Z閘(cz gate)。Xmon之結構設計使其躍遷頻率可透過外加於超導約瑟夫接面磁場調控、並以外 加電場控制y分量能量且可透過電容交互作用偶和兩Xmon。然實際情況下無論何種材料之量子位元皆非完美二能階系統，諸如環境或電 子設備造成之雜訊與量子位元本身的資訊洩漏(information leakage)皆屬無可 避免之耗散，後者為超導量子位元主要誤差來源。建模時我們以多能階Xmon為 系統，其基態(ground state)與第一激發態(first excited state)作為計算基底 (computational basis)，其餘較高能階則為洩漏能階，當資訊自計算基底躍遷 至其他能階時視為洩漏現象發生。透過改變外加電場波形與分量，我們順利 模擬出目標邏輯閘，並將誤差減少至 10^−6。運算過程中使用GOAT(Gradient Optimization of Analytic Control)演算法，並成功模擬出運算速度約 35奈秒之量 子受控Z閘、118奈秒之量子互換閘及4.5奈秒之量子反閘。

關鍵字

超導量子位元 ； Xmon ； 優化控制 ； 耗散 ； GOAT

並列摘要

Quantum computation plays an essential role in recent technology for the demands of faster and more efficient computing for complex and difficult problems. Many materials are used to build quantum computers, for example, superconductors, semi- conductors, trapped ions, optical lattice atoms, electrons, or photons. The funda- mental unit of quantum computers is called qubit. In this thesis, we focus on one of the promising candidates, superconducting Xmon, and theoretically study single and two-qubit gates in the current circuit quantum electrodynamics (QED) archi- tecture. The experiment design of Xmon follows Ref.[1] in which the two Xmons couple with each other capacitively, and the energy spacing between the ground state and the first excited state can be tuned by varying the amount of magnetic flux through superconducting Josephson junctions. The y-component Hamiltonian can also be controlled by external microwaves.
Dissipation is a serious issue for quantum computers regardless of their mate- rials. Besides, a superconducting qubit is not a perfect two-level system. Thus, most common problems are leakage to higher energy levels or electric noise from the environment and experimental apparatus. Here we consider a model of multilevel Xmons, i.e., each has more than two levels. The states of the lowest two energy levels act as computational basis of quantum bit while the higher-energy states are taken as leakage channels. In our simulation, we implement one single qubit gate, not gate, and two two-qubit gates, swap gate and cz gate. By modifying the applied microwaves on Xmons, both z- and y-components and their pulse shapes, we theoretically demonstrate optimal control pulses to achieve high-fidelity target gates using a gradient-based algorithm, Gradient Optimization of Analytic Control (GOAT). The operation times are roughly 35ns for cz gate and 4.5ns for not gate, both with similar infidelity below 10^−6. We also demonstrate a 118ns swap gate with an infidelity below 10^−4.

並列關鍵字

superconducting qubits ； Xmon ； optimal control ； leakage ； GOAT

參考文獻

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