论文标题
使用嘈杂的中间尺度量子设备的晶格量表理论和动态量子相变
Lattice gauge theory and dynamical quantum phase transitions using noisy intermediate scale quantum devices
论文作者
论文摘要
晶格量规理论是与粒子物理最基本模型有关的一种引人入胜且丰富的理论，并且随着对量子水平的实验控制的增加，对非平衡效应（例如动力学量子相变的非平衡效应）的兴趣日益增加。为了证明如何在近期量子设备中访问这些物理理论，我们研究了（1+1）d u（1）d u（1）量子链接模型的动力学。我们发现，该系统对所有系统大小都进行了动态量子相变，即使是可以通过分析求解动力学的最小的最小的量子相。我们设计了一个规格不变的字符串顺序参数，其零与Loschmidt振幅的结构相关，从而使该顺序参数可用于近期设备的实验研究。 Loschmidt振幅的零以及我们订单参数的零的零是由涡流中的，可以通过拓扑上不变的绕组数来计算的。考虑到嘈杂的中等规模量子设备，我们提出了一类超导电路，以用于U（1）量子链接模型的一般实现。这些电路的原理可以推广到实施其他更复杂的仪表对称性。此外，可以将电路模块化为任何晶格配置。使用逼真的电路参数模拟电路动力学，我们发现它以稳定的平均保真度为$ 99.5 \％$或更高。最后，我们考虑使用一种方法来考虑通过一种方法来产生有关所有自由度的信息，并仅将谐振器分散地耦合到其中的一个子集。这构成了一个直接且相对直接的协议，可以访问loschmidt振幅和顺序参数。
Lattice gauge theories are a fascinating and rich class of theories relating to the most fundamental models of particle physics, and as experimental control on the quantum level increases there is a growing interest in non-equilibrium effects such as dynamical quantum phase transitions. To demonstrate how these physical theories can be accessed in near-term quantum devices, we study the dynamics of a (1+1)D U(1) quantum link model following quenches of its mass-term. We find that the system undergoes dynamical quantum phase transitions for all system sizes considered, even the smallest where the dynamics can be solved analytically. We devise a gauge invariant string order parameter whose zeros correlates with the structure of the Loschmidt amplitude, making the order parameter useful for experimental study in near-term devices. The zeros of the Loschmidt amplitude as well as the zeros of our order parameter are revealed by vortices in their phases, which can be counted by a topologically invariant winding number. With noisy intermediate scale quantum devices in mind, we propose a class of superconducting circuits for the general implementation of U(1) quantum link models. The principles of these circuits can be generalized to implement other, more complicated gauge symmetries. Furthermore, the circuit can be modularly scaled to any lattice configuration. Simulating the circuit dynamics with realistic circuit parameters we find that it implements the target dynamics with a steady average fidelity of $ 99.5\% $ or higher. Finally, we consider readout of the circuit using a method that yields information about all the degrees of freedom with resonators coupled dispersively to only a subset of them. This constitutes a direct and relatively straightforward protocol to access both Loschmidt amplitudes and the order parameter.
