Flux-charge symmetric theory of superconducting circuits

• URL: http://arxiv.org/abs/2401.08549v1
• Date: Tue, 16 Jan 2024 18:18:52 GMT
• Title: Flux-charge symmetric theory of superconducting circuits
• Authors: Andrew Osborne and Andrew Lucas
• Abstract summary: We present a theory of circuit quantization that treats charges and flux on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to non-planar circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to circuit quantization treat fluxes and charges, which end up as the canonically conjugate degrees of freedom on phase space, asymmetrically. By combining intuition from topological graph theory with a recent symplectic geometry approach to circuit quantization, we present a theory of circuit quantization that treats charges and fluxes on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to non-planar circuits.

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