  Quantum circuit theory is a powerful and ever-evolving tool to predict the
dynamics of superconducting circuits. In its language, quantum phase slips
(QPSs) are famously considered to be the exact dual to the Josephson effect.
However, this duality renders the integration of QPS junctions into a unified
theoretical framework very difficult, and as we show, gives rise to serious
inconsistencies for different formalisms, and in some cases difficulties to
include time-dependent flux driving. We propose to resolve these issues by
reducing and compactifying the Hilbert space describing the QPS processes. Our
treatment provides for the first time a unified description of the
Aharonov-Bohm and Aharonov-Casher effects, properly defines the valid form of
inductive interactions to an environment, and allows to account for recent
insights on how to include electromotive forces. Finally, we show that the
compactification is likewise important for correctly predicting the available
computational space for qubit architectures involving QPS junctions.
