High Convergence Rates of CMOS Invertible Logic Circuits Based on Many-Body Hamiltonians

TL;DR

A Hamiltonian is created that includes three-body interaction of spins (probabilistic nodes) that provides some degrees of freedom to design a simpler landscape of Hamiltonian than that of the conventional two-body Hamiltonian.

Abstract

This paper introduces CMOS invertible-logic (CIL) circuits based on many-body Hamiltonians. CIL can realize probabilistic forward and backward operations of a function by annealing a corresponding Hamiltonian using stochastic computing. We have created a Hamiltonian that includes three-body interaction of spins (probabilistic nodes). It provides some degrees of freedom to design a simpler landscape of Hamiltonian (energy) than that of the conventional two-body Hamiltonian. The simpler landscape makes it easier to reach the global minimum energy. The proposed three-body CIL circuits are designed and evaluated with the conventional two-body CIL circuits, resulting in few-times higher convergence rates with negligible area overhead on FPGA.

Figures (7)

• Figure 1: Two-input invertible AND in one example of invertible logic: (a) two-body Hamiltonian, (b) landscape of energy (Hamiltonian), and (c) state probabilities when $Y$ is fixed to 0 at backward mode.
• Figure 2: Many-body Hamiltonians with interactions among more than two spins.
• Figure 3: Energy of two-input invertible AND ($Y=A\cap B$): (a) two-body Hamiltonian and (b) three-body Hamiltonian. The three-body Hamiltonian provides a simpler energy landscape than the two-body one.
• Figure 4: Proposed spin-gate circuit for three-body Hamiltonian based on integral stochastic computing that corresponds to \ref{['eqn:SP_3body']} with $s_i = \frac{1+m_i}{2}$.
• Figure 5: $I_0$ control for simulating invertible adders, where $I_{0min}$=2, $I_{omax}$=4, and $T$=100 are selected in this paper.