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Quantum circuit theory is a powerful and ever-evolving tool to predict thedynamics 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 unifiedtheoretical framework very difficult, and as we show, gives rise to seriousinconsistencies for different formalisms, and in some cases difficulties toinclude time-dependent flux driving. We propose to resolve these issues byreducing and compactifying the Hilbert space describing the QPS processes. Ourtreatment provides for the first time a unified description of theAharonov-Bohm and Aharonov-Casher effects, properly defines the valid form ofinductive interactions to an environment, and allows to account for recentinsights on how to include electromotive forces. Finally, we show that thecompactification is likewise important for correctly predicting the availablecomputational space for qubit architectures involving QPS junctions.

Compact description of quantum phase slip junctions