Quantum circuit theory is a powerful tool to describe superconducting circuits. In its language, quantum phase slips (QPSs) are considered to be the exact dual to the Josephson effect. This duality renders the integration of QPS junctions into a unified theoretical framework challenging. As we argue, different existing formalisms may be inconsistent, and the correct inclusion of time-dependent flux driving requires introducing a large number of auxiliary, nonphysical degrees of freedom. We resolve these issues by describing QPS junctions as inductive rather than capacitive elements, and reducing the Hilbert space to account for a compact superconducting phase. Our treatment provides an approach to circuit quantization exclusively in terms of node-flux-node variables, and eliminates spurious degrees of freedom. Finally, the inductive treatment reveals the possibility of a voltage-dependent renormalization of the QPS amplitude, by accounting for spatial variations of the electric field built up across the junction.

量子电路理论是描述超导电路的有力工具。用其语言来说，量子相滑（QPS）被认为是约瑟夫森效应的精确对偶。这种二元性使得将 QPS 连接集成到统一的理论框架中具有挑战性。正如我们所说，不同的现有形式主义可能不一致，并且正确包含依赖时间的磁通驱动需要引入大量辅助的、非物理的自由度。我们通过将 QPS 结描述为电感元件而不是电容元件，并减小希尔伯特空间以考虑紧凑的超导相来解决这些问题。我们的处理提供了一种专门根据节点-通量-节点变量进行电路量化的方法，并消除了虚假的自由度。最后，通过考虑结点上建立的电场的空间变化，感应处理揭示了 QPS 幅度的电压依赖性重整化的可能性。