Reciprocal lumped-element superconducting circuits: quantization, decomposition, and model extraction

TL;DR

This paper presents new methods for quantizing, decomposing, and extracting superconducting circuit models using network matrices, enabling better analysis and design of quantum devices with Josephson junctions and phase slip wires.

Contribution

The authors introduce a network matrix-based framework for circuit quantization, decomposition, and model extraction from electromagnetic simulations, advancing superconducting quantum circuit analysis.

Findings

Demonstrated a simple algorithm for circuit quantization with novel Hamiltonian predictions.

Developed pivoting operations to decompose circuits into fundamental forms.

Provided a method to extract exact circuit models from electromagnetic simulation data.

Abstract

In this work, we introduce new methods for the quantization, decomposition, and extraction (from electromagnetic simulations) of lumped-element circuit models for superconducting quantum devices. Our flux-charge symmetric procedures center on the network matrix, which encodes the connectivity of a circuit's inductive loops and capacitive nodes. First, we use the network matrix to demonstrate a simple algorithm for circuit quantization, giving novel predictions for the Hamiltonians of circuits with both Josephson junctions and quantum phase slip wires. We then show that by performing pivoting operations on the network matrix, we can decompose a superconducting circuit model into its simplest equivalent "fundamental" form, in which the harmonic degrees of freedom are separated out from the Josephson junctions and phase slip wires. Finally, we illustrate how to extract an exact, transformerless circuit model from electromagnetic simulations of a device's hybrid admittance/impedance response matrix, by matching the lumped circuit's network matrix to the network topology of the physical layout. Overall, we provide a toolkit of intuitive methods that can be used to construct, analyze, and manipulate superconducting circuit models.