Circuit Quantisation in Hamiltonian Framework: A Constraint Analysis Approach

TL;DR

This paper applies Dirac's Constraint Analysis to superconducting quantum circuits, providing a systematic Hamiltonian approach to identify canonical variables for quantization, improving robustness over existing methods.

Contribution

It introduces a Hamiltonian constraint analysis method for circuit quantization, offering a more general and robust framework compared to previous techniques.

Findings

Successfully isolates canonical degrees of freedom in SQCs

Demonstrates robustness of DCA over other methods

Provides a systematic approach for circuit quantization

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.