Solving Superconducting Quantum Circuits in Dirac's Constraint Analysis Framework
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912080457629696 |
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| author | Pandey, Akshat Ghosh, Subir |
| author_facet | Pandey, Akshat Ghosh, Subir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_10611 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Solving Superconducting Quantum Circuits in Dirac's Constraint Analysis Framework Pandey, Akshat Ghosh, Subir Quantum Physics Mesoscale and Nanoscale Physics High Energy Physics - Theory 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. |
| title | Solving Superconducting Quantum Circuits in Dirac's Constraint Analysis Framework |
| topic | Quantum Physics Mesoscale and Nanoscale Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.10611 |