Symplectic geometry and circuit quantization

Abstract

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 the standard 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 circuits, including those that cannot be quantized using existing methods.

30 pages, 8 figures

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Cited by in corpus (13)

• Quantum circuits with multiterminal Josephson-Andreev junctions
• Geometrical description and Faddeev-Jackiw quantization of electrical networks
• A Review of Design Concerns in Superconducting Quantum Circuits
• Lecture Notes on Quantum Electrical Circuits
• Clifford operations and homological codes for rotors and oscillators
• Exact quantization of nonreciprocal quasi-lumped electrical networks
• Flux-charge symmetric theory of superconducting circuits
• Stochastic theory of nonlinear electrical circuits in thermal equilibrium
• Circuit Quantisation from First Principles
• Viewing protected superconducting qubits through the lens of the cat qubit
• Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits
• Improving the accuracy of circuit quantization using the electromagnetic properties of superconductors
• Utilizing discrete variable representations for decoherence-accurate numerical simulation of superconducting circuits