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arXiv · 2308.10611

Solving Superconducting Quantum Circuits in Dirac's Constraint Analysis Framework

Akshat Pandey·Subir Ghosh
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Abstract

In this work we exploit Dirac's Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} way. 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 via a generalized Correspondence Principle. This purely algebraic approach makes the application of concepts such as graph theory, null vector, loop charge,\ etc that are in vogue, (each for a specific type of circuit), completely redundant. The universal validity of DCA scheme in SQC, proposed by us, is demonstrated by correctly re-deriving existing results for different SQCs, obtained previously exploiting different formalisms each applicable for a specific SQC. Furthermore, we have also analysed and predicted new results for a generic form of SQC - it will be interesting to see its validation in an explicit circuit implementation.

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Akshat Pandey, Subir Ghosh. 2023-08-21. Solving Superconducting Quantum Circuits in Dirac's Constraint Analysis Framework. https://arxiv.org/abs/2308.10611

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