Circuits and systems modeling of quantum systems in SPICE

Abstract

Quantum systems are entering a crucial stage of technology development where it is critical that design automation tools are co-developed along with the technology itself. Electronics design ecosystem provides tools which may be extended towards simulation and verification, critical steps towards large-scale certifiable designs of such quantum systems. SPICE simulations provide an appropriate level of abstraction that is both physical, in terms of custom designed physical components, and simulation approach, i.e. differential-algebraic equations. In this work we describe our efforts in modeling quantum + classical systems within SPICE. We first present our highly successful spintronics platform that has allowed us to model a multitude of spintronic effects including transport in tunnel-junctions, full lifecycle of quasi-quantum topological objects such as skyrmions, and transport in topological materials (TI, Weyl Semimetals). We demonstrate the extension of this platform towards simulations of circuits built using spin-qubits made from Josephson junctions, and a more emergent platform of Majorana Zero Modes (MZMs). We describe our approach that allows us to abstract away microscopic details, while capturing device and circuit behavior using controlled sources and custom components. We describe our approach to embed full dynamic solutions of alternate non-electrical state variables and indeed abstract quantities within the framework of SPICE. Our approach interplays well with more “fundamental” modeling approaches such as quantum master equations and non-equilibrium Green’s functions, as well as more “system” level modeling approaches such as SystemVerilog, thereby bridging both these worlds for exploration, analysis, simulation, and verification of scaled quantum systems.