Classical Circuit Simulations for Superconducting Quantum Circuits

Qubits based on superconducting circuits are being actively developed for quantum computing. Superconducting circuits with the same elements are also used for classical electronic circuits, and are simulated using standard classical circuit simulation tools. The theory of quantum circuits requires fundamental uncertainty, superposition, and entanglement, which are not included in classical models. For this reason, few quantum experiments make comparisons to classical simulations. However, some researchers have shown that classical simulations of superconducting circuits can account for observations on Josephson junctions that have otherwise been attributed to uniquely quantum effects [1]. This analysis is extended here to coupled superconducting oscillators, which are similar to quantum circuits explored in experiments. Classical circuit simulations of complex superconducting circuits can be readily carried out, and can be compared to measurements of coupled superconducting qubits. In this way, it may be possible to more clearly distinguish true quantum effects from those which may have a classical explanation.
[1] J.A. Blackburn, et al, “A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures,” Phys. Rep. 611, 1 (2016)