[论文解读] Analytical Solutions for N-Electron Interacting System Confined in Graph of Coupled Electrostatic Semiconductor and Superconducting Quantum Dots in Tight-Binding Model with Focus on Quantum Information Processing

Krzysztof Pomorski, Robert Bogdan Staszewski|arXiv (Cornell University)|Jul 6, 2019

Quantum and electron transport phenomena参考文献 20被引用 16

一句话总结

本文提出了一种基于紧束缚模型的解析解，用于研究耦合半导体与超导量子点中N电子相互作用系统的量子门控制，实现了对基于位置的量子比特的精确调控。推导了量子门（Hadamard门、相位旋转门）的解析表达式，通过电磁腔实现了非局域纠缠，并建立了半导体与超导量子比特之间的静电接口——这些成果对混合量子计算和量子互联网架构具有重要意义。

ABSTRACT

Analytical solutions for a tight-binding model are presented for a position-based qubit and N interacting qubits realized by quasi-one-dimensional network of coupled quantum dots expressed by connected or disconnected graphs of any topology in 2 and 3 dimensions where one electron is presented at each separated graphs. Electron(s) quantum dynamic state is described under various electromagnetic circumstances with an omission spin degree-of-freedom. The action of Hadamard and phase rotating gate is given by analytical formulas derived and formulated for any case of physical field evolution preserving the occupancy of two-energy level system. The procedure for heating up and cooling down of the quantum state placed in position based qubit is described. The interaction of position-based qubit with electromagnetic cavity is described. In particular non-local communication between position based qubits is given. It opens the perspective of implementation of quantum internet among electrostatic CMOS quantum computers (quantum chips). The interface between superconducting Josephson junction and semiconductor position-based qubit implemented in coupled semiconductor q-dots is described such that it can be the base for electrostatic interface between superconducting and semiconductor quantum computer. Modification of Andreev Bound State in Josephson junction by the presence of semiconductor qubit in its proximity and electrostatic interaction with superconducting qubit is spotted by the minimalistic tight-binding model. The obtained results allow in creating interface between semiconductor quantum computer and superconducting quantum computer. They open the perspective of construction of QISKIT like software that will describe both types of quantum computers as well as their interface.

研究动机与目标

• 在电磁场作用下，为耦合量子点中的N电子系统推导解析解。
• 通过半导体量子点中电压门控的静电势，实现对基于位置的量子比特的精确控制。
• 在紧束缚模型中，为两能级系统制定解析的量子门（Hadamard门、相位旋转门）。
• 建立半导体与超导量子比特之间的功能性静电接口，以支持混合量子计算。
• 通过电磁腔和波导实现非局域量子通信与纠缠，用于量子互联网应用。

提出的方法

• 为具有任意2D/3D拓扑结构的耦合量子点准一维网络构建紧束缚哈密顿量模型。
• 在外部电磁场作用下，推导时间演化算符与密度矩阵的解析解。
• 应用拉比振荡形式化方法，对两能级系统中的相干叠加与门操作进行建模。
• 通过库仑势和弱测量协议，对量子比特之间的静电相互作用进行建模。
• 利用极简化的紧束缚模型，将约瑟夫森结与半导体量子比特集成，以描述Andreev束缚态。
• 结合解析与数值方法，模拟电容耦合的单电子线（SEL），并测量量子态动力学。

实验结果

研究问题

• RQ1 能否为在任意电磁环境下的耦合量子点中N电子相互作用系统推导出解析解？
• RQ2 如何通过电压控制的势垒隧穿幅度，在紧束缚模型中实现Hadamard门与相位旋转门的解析控制？
• RQ3 通过电磁腔耦合，空间分离的基于位置的量子比特之间非局域纠缠的机制是什么？
• RQ4 半导体量子比特与约瑟夫森结之间的静电耦合如何改变Andreev束缚态？
• RQ5 是否能构建一个完全解析的框架，描述耦合单电子线及其与飞行量子比特相互作用的动力学？

主要发现

• 推导出在任意电磁场作用下，两能级基于位置的量子比特的时间演化算符与密度矩阵的解析表达式。
• 通过紧束缚模型中电压驱动的隧穿幅度解析控制，实现了Hadamard门与相位旋转门。
• 通过电磁腔耦合，展示了远距离基于位置的量子比特之间的非局域纠缠，实现了远距离量子通信。
• 通过解析本征能级计算，表明半导体量子比特与约瑟夫森结之间的静电相互作用会改变Andreev束缚态谱。
• 半导体与超导量子比特之间的接口被解析描述，支持混合量子计算架构的实现。
• 对两个耦合的单电子线的弱测量协议进行了解析建模，推导出量子与经典情况下的反相关函数。