Enumeration of all superconducting circuits up to 5 nodes

TL;DR

This paper systematically catalogs all superconducting circuits with up to five nodes, providing a comprehensive resource for discovering new circuit configurations for quantum computing and related applications.

Contribution

It introduces a method to enumerate and classify all small superconducting circuits, including a novel concept of Hamiltonian classes, aiding future circuit design.

Findings

Identified all unique circuits up to five nodes using graph isomorphism.

Classified circuits based on Hamiltonian structures and variable types.

Provided a database of circuits as a resource for qubit design.

Abstract

Nonlinear superconducting circuits can be used as amplifiers, transducers, and qubits. Only a handful of superconducting circuits have been analyzed or built, so many high-performing configurations likely remain undiscovered. We seek to catalog this design space by enumerating all superconducting circuits -- up to five nodes in size -- built of capacitors, inductors, and Josephson junctions. Using graph isomorphism, we remove redundant configurations to construct a set of unique circuits. We define the concept of a ``Hamiltonian class'' and sort the resulting circuit Hamiltonians based on the types of variables present and the structure of their coupling. Finally, we search for novel superconducting qubits by explicitly considering all three node circuits, showing how the results of our enumeration can be used as a starting point for circuit design tasks.