Demonstration of Superconductor Shift Registers with Energy Dissipation Below Landauer's Thermodynamic Limit

Abstract

We study energy dissipation and propagation of information encoded by Josephson vortices in two types of circular shift register: a) a uniform register composed of sections of discrete Josephson transmission lines (JTL) forming a closed loop with a flux pump allowing to change the number of moving fluxon; b) a nonuniform register composed of sections of the regular JTL and sections of JTLs utilizing nSQUIDs - dc-SQUIDs with negative inductance between their arms - instead of single Josephson junctions. nSQUIDs are parametric devices with a flexible double-well potential that were proposed as components for reversible computing. For the uniform register, we demonstrate the energy dissipation per bit-shift operation below the Landauer's thermodynamic limit $E_T=k_BTln2$ up to propagation delays of ~0.7 ns, corresponding to the circular information motion with frequencies up to ~1.4 GHz. This does not contradict Landauer's minimum energy requirement for computations since information is not destroyed. For the nonuniform register, we find the minimum energy dissipation per bit-shift of about 16$E_T$ and attribute this to a nonuniform movement of vortices and energy barriers between the regular JTL and nSQUID sections. Differences of Josephson vortex propagation in both types of circular registers are discussed based on the measured current-voltage characteristics, extracted effective resistance and the terminal speed of Josephson vortices, and their dependences on the number of moving vorticies. nSQUID inductance connecting JJs to the ground leads to an unusual type of lossless discrete transmission line with frequency-dependent impedance and propagation speed, both different from the regular JTLs.