Demonstration of Bit-Serial SFQ-Based Computing for Integer Iteration Algorithms

The Collatz conjecture asserts that by a repeated iteration rule, the operation starting from any positive integer n, eventually produces the value of “1.” The main contribution of this paper is to demonstrate a single-flux-quantum (SFQ)-based hardware algorithm that performs an exhaustive search to verify the Collatz conjecture. The circuit consists of a 16-bit integer register, a high-frequency clock generator, and a central processor. This design can perform at up to a maximum clock frequency of 90 GHz with a total power consumption of about 0.85 mW in simulation, based on the AIST 10 kA/cm
²
advanced Nb process. An LR-biasing approach further reduces the power consumption, whereas the computing speed can be accelerated by a factor of 20 when accelerating approaches are adopted. The assessments show that our design can process 2 × 10
⁷
numbers every second with an energy efficiency of about 5 × 10
¹⁰
numbers per Joule.