基于超导电路系统的量子模拟

量子多体系统是由多个相互作用粒子组成的物理系统，它的希尔伯特空间会 随着系统尺寸增加而指数增加，是数值模拟中最具挑战性的研究对象之一。过去， 研究人员试图使用各种技术来模拟这些系统，包括蒙特卡罗模拟，甚至精确对角 化。1982 年 Feynman 提出是否能做出一个量子计算机，它能模拟量子系统。量子 计算机模拟量子系统按原理来分有两种类型：数值量子模拟和类比量子模拟。本论 文主要基于超导电路量子化理论设计超导电路，使该电路能够类比量子模拟 BoseHubbard 模型和 Su-Schrieffer-Heeger(SSH) 模型。以 Transmon 为耦合器，连接两个 改造后的 C-shunt 磁通量子比特，组合成 CSFQ-Transmon-CSFQ 电路，该电路在同 一参数下可以实现：1、抑制最近邻比特间的 XY 相互作用下，ZZ 相互作用强度还 能达到几十 MHz 的量级；2、抑制 ZZ 相互作用的同时，还可以调节 XY 相互作用强 度；3、XY 和 ZZ 相互作用强度还可调节至量级相当。拓展 CSFQ-Transmon-CSFQ 电路，设计电路 CSFQ-Transmon 链具有多可调自由度的特点，在同一电路参数下： 1、改造后的 C-shunt 磁通量子比特的频率和非谐性同时可调，并且非谐性可以连 续地从负值调到正值；2、次近邻比特间的耦合强度远远小于最近邻比特间的耦合 强度，最近邻比特间的耦合强度可以连续地从负值调到正值。超导量子电路可调 控、易扩展，有潜力成为研究多体量子系统的实验平台。

Quantum multi-body system is a physical system composed of multiple interacting particles. Its Hilbert space will increase exponentially with the increase of system size. It is one of the most challenging research objects in numerical simulation. In the past, researchers have tried to use various techniques to simulate these systems, including Monte Carlo simulation and even accurate diagonalization. In 1982, Feynman proposed whether we can make a quantum computer, which can simulate quantum systems. Quantum computer simulate quantum system which can be divided into two types according to the principle: numerical quantum simulation and analog quantum simulation. This paper mainly designs the superconducting circuit based on the quantization theory of superconducting circuit, which circuit can simulate the Bose-Hubbard model and Su-SchriefferHeeger (SSH) model by analogy. With Transmon as the coupler, two modified C-shunt flux qubits are connected and combined into a CSFQ-Transmon-CSFQ circuit. The circuit can realize under the same parameters: 1. Under the suppression of XY interaction between nearest neighbors, the intensity of ZZ interaction can reach the order of tens of MHz; 2. While restraining ZZ interaction, XY interaction intensity can also be adjusted; 3. The intensity of XY and ZZ interaction can also be adjusted to the same order of magnitude. Expand the CSFQ-Transmon-CSFQ circuit and design the CSFQ-Transmon chain which has the characteristics of multiple adjustable degrees of freedom. Under the same circuit parameters: 1. The frequency and anharmonicity of the modified C-shunt flux qubit are adjustable at the same time, and the anharmonicity can be continuously adjusted from negative value to positive value; 2. The coupling strength between the next nearest neighbor qubits is much less than that between the nearest neighbor qubits, and the coupling strength between the nearest neighbor qubits can be continuously adjusted from negative to positive. Superconducting quantum circuits are adjustable and easy to expand, which has the potential to become an experimental platform for the study of multi-body quantum systems.

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