circuits, rather than the phase-dependent circuits such as Josephson junction circuits and quantum-phase-slip (QPS) junction circuits. in the age of artificial intelligence (AI), we present an electromagnetic-field-based circuit theory to unify the phase-independent and phase-dependent electric circuits. This theory drives two general system models for all electric circuits, and visualizes the dynamics of circuit devices with electric-charge-flow (ECF) diagrams and the magnetic-flux-flow (MFF) diagrams. ECF and MFF diagrams enable electric circuits to be designed and analyzed like the molecules composed of two kinds of atoms; they are promising for the language to train AI-aided electronic-design-automation (EDA) tools.

integrated circuit, and are widely applied for subtle magnetic-field measurements, energy-efficient computing, and quantum computing, respectively. They are Josephson junction networks composed of Josephson junctions and normal resistor-inductor-capacitor (RLC) components, working with the fluxoid-quantization principle and Josephson effects to achieve unique flux-modulated dynamics and characteristics; they react to the vector potential of magnetic fields rather than the electric potential. However, the conventional circuit diagrams and nodal analysis methods focus on the electric charges flowing though branches and nodes, ignoring dynamics of the magnetic fluxes flowing from loop to loop. This article introduces a general flux-based circuit theory to unify the analyses of Josephson junction circuits and normal RLC circuits. This theory presents a magnetic-flux-generator (MFG) concept to unify Josephson junctions and normal circuit elements, and abstract both Josephson junction circuits and normal RLC circuits as MFG network; it derives a general network equation to describe dynamics of Josephson junction circuits, and invents a kind of magnetic-flux flow (MFF) diagram to depict the working principles of magnetic-flux flows inside Josephson junction circuits. The flux-based theory is complementary to the conventional circuit theories in the design and analysis of superconductor integrated circuits.

circuit composed of Josephson junctions and superconducting loops. However, the analysis is usually based on superconducting physics rather than the conventional circuit theorems. This article presents a general circuit analysis method using only the conventional circuit variables and laws to simplify the analysis and simulation of SQUID circuits. The method unifies the descriptions of Josephson junctions and non-superconducting elements with a general non-linear inductance concept; and derives the uniform SQUID circuit equations with the common circuit laws used for both superconducting and normal circuits. The uniform circuit equation and dynamic model show that the only element making the SQUID distinct from the non-superconducting circuits is the cosine potential introduced by the Josephson current. This general analysis method bridges the gap between the superconductive SQUID circuits and the conventional normal circuits for the electronics engineers trained with the conventional circuit theory.