量子计算是利用量子纠缠、量子态叠加进行信息处理的新型计算方式，对某些问题的处理能力大大超越了经典计算。它的发展有望引发新技术革命，为密码学、大数据和机器学习、人工智能、化学反应计算、材料设计、药物合成等许多领域的研究，提供前所未有的强力手段。本文基于超导量子电路，对超导量子电路的拓扑仿真模型的构建、拓扑量子态的仿真以及环境对拓扑态的影响进行了深入的研究。主要的研究内容和研究成果包括以下三部分：首先，我们研究了基于超导量子电路的Su-Schrieffer-Heeger（SSH）模型拓扑仿真及环境对SSH系统的影响。我们用超导量子比特电路构建了SSH模型，并在此基础上对系统的近邻格点间引入共有环境。我们发现近邻量子比特之间的共有环境会诱导比特间的耗散耦合，这种耦合会改变系统的拓扑相变点，使边界态具有复数化的隧穿因子，从而导致有限长SSH模型中边界态能量的振荡。此外，借助于微波谐振腔，我们提出了探测边界态能量振荡现象的理论方案。其次，我们研究了利用超导量子电路仿真Kitaev模型的可行性以及环境对Kitaev系统的影响。我们从理论上提出了一种利用超导量子比特电路构建Kitaev模型的方法，通过在辅助耦合环路和量子比特电路中运用含时磁通频率匹配的方法实现模型参数的独立调节。进一步，我们考虑近邻量子比特间的共有环境对Kitaev模型的影响，我们发现共有环境同样会诱导Kitaev模型近邻量子比特间出现耗散耦合，这种耦合会显著改变Kitaev模型的拓扑特性。如果所有近邻量子比特间都存在耗散耦合，它们会改变系统拓扑相变点和本征态布居分布。如果耗散耦合只存在于特定位置，则近零能态数和能谱虚部随耗散耦合位置的变化而发生改变。最后，我们将环境扩展到更接近实际的情景中，研究有限温度环境对系统量子性质的影响。特别是我们利用超导量子比特和表面声波谐振腔构造了电路量子声动力学系统，研究了环境温度对该系统量子性质的影响。我们发现随着环境温度升高，系统的量子性质会变得越来越差，当温度升高到一定值时，系统的性质从量子转变到经典。我们通过主方程给出了解析公式，成功解释了该转变的物理机制。

Quantum computing is a new way of information processing using quantum entanglement and superposition of quantum states, and its ability to deal with some problems has greatly exceeded that of classical computing. The development of quantum computing is expected to lead a new technological revolution, providing powerful means for research in many fields, such as cryptography, big data and machine learning, artificial intelligence, chemical reaction calculation, material design, and drug synthesis. Based on superconducting quantum circuits, the construction of topological model through superconducting quantum circuits, the simulation of topological quantum states and the influence of environment on topological states are deeply studied. The main research contents and results are devided into the following three parts:Firstly, we study the topological simulation of Su-Schrieffer-Heeger (SSH) model based on superconducting quantum circuit and the influence of environment on SSH model. We construct an SSH model using superconducting qubit circuits, and then introduce the common environment to the neighboring qubits of system. We find that the common environment between the neighboring qubits induces the dissipative coupling between the qubits, which changes the topological phase transition point of the system. Besides that, the dissipative coupling will make the effective localization factor of edge states become complex, and lead to the oscillation of edge states energy. In addition, we propose an theoretical scheme to detect edge state energy oscillation using microwave resonators.Secondly, we study the feasibility of the simulation of Kitaev model using superconducting quantum circuit and the influence of environment on Kitaev model. We propose a theoretical method to construct Kitaev model using superconducting qubit circuits. The parameters of the model can be adjusted independently via the frequency matching between time-dependent magnetic fluxes through the couplers and the coupled pairs of the qubits. Further, we consider the influence of the common environment on the Kitaev model, and we find that the common environment will induce dissipative coupling between neighboring qubits, which will significantly change the topological properties of the Kitaev model. If there exist dissipative couplings between all neighboring qubits, they will change the topological phase transition points and the population distribution of eigenstates. If the dissipative coupling exists only at a specific position, the number of near-zero energy states and the imaginary part of the energy spectrum change with the variation of the position of dissipative couplings.Finally, we extend the environment to a more realistic scenario and study the influence of finite-temperature environment on the quantum property of system. Here, we construct the circuit quantum acousticdynamic system using superconducting qubit and surface acoustic wave resonator, and study the effect of temperature on the quantum properties of this system. We find that the quantum property of system becomes more and more weak with the increasing of temperature, the property of system will change from quantum to classical when the temperature get increased to a certain extent. We obtain the analytical formula through the master equation, and explain the physical mechanism of the transformation successfully.