Abstract: Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose degrees of freedom are either magnetic fluxes or electric charges in the circuit. By combining nonlinear circuit elements, it is possible to build circuits where a standard Lagrangian description does not exist.
We have found an alternative formalism for circuit quantization, by discovering an intrinsically Hamiltonian formulation of the classical mechanics of a circuit. This formulation enables the quantization of circuit which could not be analyzed using existing frameworks. This Hamiltonian formulation also makes famous circuit dualities manifest