Circuit Quantisation in Hamiltonian Framework: A Constraint Analysis Approach

Abstract: In this work we apply Dirac's Constraint Analysis (DCA) to solve Superconducting Quantum Circuits (SQC). The Lagrangian of a SQC reveals the constraints, that are classified in a Hamiltonian framework, such that redundant variables can be removed to isolate the canonical degrees of freedom for subsequent quantization of the Dirac Brackets. We demonstrate the robustness of DCA unlike certain other set of ideas like null vector and loop charge which are each applicable only to specific types of quantum circuits.