Demonstration of Superconductor Shift Registers With Energy Dissipation Below Landauer’s Thermodynamic Limit

We study energy dissipation and propagation of information encoded by Josephson vortices in two types of circular shift registers: a) uniform registers composed of sections of discrete Josephson transmission lines (JTL) forming a closed loop with a flux pump allowing us to change the number of moving fluxons; b) nonuniform registers 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 (JJs). 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 E2=KBT In2 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 16ETand 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 vortices. 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.