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Symplectic geometry and circuit quantization



Andrew Osborne, Trevyn Larson, Sarah Jones, Raymond Simmonds, Andras Gyenis, Andrew Lucas


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 (such as Josephson junctions or quantum phase slips), it is possible to build circuits where a standard Lagrangian description (and thus quantization method) does not exist. Inspired by the mathematics of symplectic geometry and graph theory, we address this challenge, and present a Hamiltonian formulation of non-dissipative electrodynamic circuits. The resulting procedure for circuit quantization is independent of whether circuit elements are linear or nonlinear, or if the circuit is driven by external biases. We explain how to re-derive known results from our formalism, and provide an efficient algorithm for quantizing all LC circuits, including those that cannot be quantized using existing methods.


Superconducting Circuits, Quantization, Symplectic


Osborne, A. , Larson, T. , Jones, S. , Simmonds, R. , Gyenis, A. and Lucas, A. (2023), Symplectic geometry and circuit quantization, arxiv, [online], (Accessed May 18, 2024)


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Created April 17, 2023, Updated May 11, 2023