Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories.

模拟量子模拟有可能成为研究复杂量子系统中必不可少的技术。在这项工作中，我们以数字方式研究了一个基于约瑟夫森结的一维，忠实，模拟，量子电子电路模拟器，用于可积量子场论的范式模型之一：1+中的量子正弦-戈登（qSG）模型1时空维度。我们使用密度矩阵重归一化组技术分析晶格模型，并使用现有的Bethe ansatz计算对我们的数值结果进行基准测试。此外，我们对顶点算子的两点相关函数进行了解析形式因子计算，这与我们的数值计算非常吻合。最后，我们计算了qSG模型的纠缠谱。我们将结果与使用基于量子XYZ链的可积晶格正则化所获得的结果进行了比较，结果表明，与XYZ链相比，量子电路模型更不容易进行缩放校正。我们提供的数字证据表明，通过现代超导电路技术可以访问实现qSG模型所需的参数，从而进一步证明了后者用于模拟强相互作用的量子场论的平台的可行性。