基于量子点自旋比特实现高保真几何量子门

     量子计算利用量子力学的基本原理，具备远超经典计算机的计算能力，可以解
决经典计算机难以解决的实际问题。量子计算机的实现需要可靠的物理体系。半
导体量子点量子比特具有相干时间长、可拓展、易于集成的优势，是最有希望实
现通用量子计算机的物理体系之一。然而，为了实现容错量子计算，基于半导体
量子点自旋比特制备量子门的保真度还需要进一步提升。本论文提出基于半导体
量子点自旋量子比特实现几何量子门的方案，可以有效的抵抗开放系统与环境相
互作用引起的退相干和操作误差。
    本论文致力于半导体量子点量子比特的高保真度几何量子逻辑门的理论研究，
主要工作有：
    一、提出基于半导体量子点电子自旋量子比特制备非绝热几何量子门的方案。
我们优化了单回路橘形演化路径的方案，设计一般的单回路橘形演化路径来实现
非绝热几何量子门。通过计算量子门的演化时间和鲁棒性分析，我们的方案具备
以下优势：一是降低量子门的演化时间，二是提高了量子门的保真度，三是可以在
对称的双量子点系统中，通过电偶极子自旋共振技术驱动量子比特，直接实现控
制非门。
    二、提出基于半导体量子点单-三态自旋量子比特制备非绝热和乐量子门的方
案。在该方案中，我们制备了𝑅𝑧(𝜋(1 + sin 𝛾)) 量子门和𝑅𝑥(𝜋(1 + sin 𝛾)) 量子门。
进一步，结合这两个量子门可以实现任意的非绝热单比特和乐量子门。

    Quantum computation has far more powerful computing capabilities than classical computation, and can solve practical problems that are difficult to be solved by classical computer, utilizing the basic principles of quantum mechanics. To realize quantum computer, it requires reliable physical systems. Semiconductor quantum dots with long coherence time and scalability, is one of the most promising physical systems to realize
universal quantum computer. However, to realize fault-tolerant quantum computation, the fidelity of quantum gates based on spin qubits in quantum dots needs to be further improved. In this thesis, we propose a scheme to realize high fidelity geometric quantum gates based on spin qubits in semiconductor quantum dots, which can effectively resist the
decoherence and operation error, that are caused by the interaction between open system and environment.
    This thesis is devoted to the theoretical research of high fidelity geometric quantum gates of spin qubits in semiconductor quantum dots. The main achievements are the following:
    1. A scheme for realizing non-adiabatic geometric quantum gates based on spin qubits in semiconductor quantum dots is proposed. We optimize the scheme of orangeslice-sharped-loops evolution path, and design a general-orange-slice-sharped-loop evolution path to achieve non-adiabatic geometric quantum gate. By calculating the evolution time and analyzing the robustness, the advantages of our scheme are the following: first, it reduces the evolution time of quantum gates; second, it improves the fidelity of quantum gates; third, it can drive qubits through electric dipole spin resonance technology in a symmetrical double quantum dot system to directly realize the CNOT gate.
    2. A scheme for realizing non-adiabatic geometric quantum gates based on singlettriplrt spin qubits in semiconductor quantum dots is proposed. In the scheme, we realize the 𝑅𝑧(𝜋(1 + sin 𝛾)) and 𝑅𝑥(𝜋(1 + sin 𝛾)) gates. Furthermore, arbitrary non-adiabatic holonomic single-qubit gates can be realized by combining 𝑅𝑧(𝜋(1+sin 𝛾)) and 𝑅𝑥(𝜋(1+sin 𝛾)) gates.

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