Algebraic canonical quantization of lumped superconducting networks

TL;DR

This paper introduces a systematic method for the canonical quantization of lumped superconducting networks using symplectic diagonalization, enabling accurate quantum descriptions of complex electrical systems.

Contribution

It provides a novel, constructive algorithm for quantizing superconducting networks via symplectic diagonalization, extending black-box quantization and Landau quantization techniques.

Findings

Successfully quantized singular electrical networks

Extended black-box quantization to nonreciprocal systems

Demonstrated the method with Landau quantization example

Abstract

We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive implementation of the symplectic diagonalization of positive semidefinite Hamiltonian matrices, a particular instance of Williamson's theorem. With it, we derive canonically quantized discrete-variable descriptions of passive causal systems. We exemplify the algorithm with representative singular electrical networks, a nonreciprocal extension for the black-box quantization method, as well as an archetypal Landau quantization problem.