Classically reversible logic gate coupled to a superconducting qubit: Problem definition (pt. 1)

New research is starting on a digital logic that uses physical and logical reversibility to achieve higher energy efficiency than commercial digital gates which are irreversible. After describing resonant dynamics of topological solitons in classical reversible superconducting gates, we discuss the theoretical coupling to a superconducting qubit. The solitons in this classical logic are fluxons in Long Josephson Junctions (LJJs), and the fluxon polarity (fluxon or antifluxon) represents a bit state. Gate structures consist of input and output LJJs, and a JJ circuit interface in-between is such that an incoming fluxon temporarily exchanges energy with a localized mode, before an output fluxon emerges with operation-defined polarity. This scattering is efficient and fast in 1- and 2-bit gates. While quantum fluctuations are intentionally negligible for classical gate operations, we study fluxon gates coupled with a qubit, as a possible resource for qubit readout. We analyze the gates with a quasiparticle model for the LJJ fields. Depending on the exact interface design, different types of elastic scattering occur. In a quantum regime, with a qubit embedded across the central interface JJ, a quantized version of the quasiparticle model should be a convenient approximation.