Landauer-Limited Dissipation in Quantum-Flux-Parametron Logic

Abstract

The Landauer limit is to irreversible logic what the Carnot cycle is to heat engines. This limit is approached in the adiabatic Quantum Flux Parametron (aQFP) by copying the inputs of standard logic gates to produce reversible logic gates, and disposing of the copied inputs using the "terminate" gate dissipating only the thermal energy, ln2$kT$. This method eliminates the non-adiabatic switching associated with backaction that arises in conventional aQFP logic. Real aQFP devices have parameter mismatch causing proportionate increases in dissipation and bit-error rate. A chip with $10^9$ aQFPs with realistic fabrication spread of 1%-1$\sigma$ control on junction critical current and 5%-1$\sigma$ on inductors would have outlier devices with a bit-error rate of $10^{-31}$, compared to $10^{-71}$ for ideal devices. Power dissipation across all devices on-chip would increase to about 7$\times$ the Landauer limit. An ideal circuit processing correlated bit streams dissipates fractional bit energy per cycle commensurate with the information lost, in accord with Landauer's concept of logical entropy.