Extended-variable probabilistic computing with probabilistic d-dimensional bits

Ising machines can solve combinatorial optimization problems by representing them as energy minimization problems. A common implementation is the probabilistic Ising machine (PIM), which uses probabilistic (p-) bits to represent coupled binary spins. However, many real-world problems have complex data representations that do not map naturally into a binary encoding, leading to a significant increase in hardware resources and time-to-solution. Here, we describe a generalized spin model that supports an arbitrary number of spin dimensions, each with an arbitrary real component. We define the probabilistic d-dimensional bit (p-dit) as the base unit of a p-computing implementation of this model. We further describe two restricted forms of p-dits for specific classes of common problems and implement them experimentally on an application-specific integrated circuit (ASIC): (A) isotropic p-dits, which simplify the implementation of categorical variables resulting in ~34x performance improvemen..., ASIC design
The ASIC PIM was defined using RTL Verilog code which was processed by the OpenLane RTL to GDSII pipeline, using the Skywater 130 nm open-source process design kit (PDK). The PIM was manufactured using the Efabless multi-project wafer (MPW) service, which also provided the design for a co-integrated small CPU based on a VexRiscv minimal+debug configuration [61]. An oscillator running at 10 MHz was used as the ASIC’s clock for all experiments shown.
Experimental code
All non-trivial problems and their Ising representations were created using self-made Python 3 code. All simulated data were gathered using self-made C++ code. Self-made C code executed on the RISC-V CPU was used to run all experimental trials. Communication with the RISC-V CPU, to upload trial code and to record results, was done using the UART protocol over a USB cable.
IQP Comparison
Solvers used for the IQP comparison were bundled with GAMS 49.3.0 [62] and accessed using GAMS Studio 1.20.2. To the best of our..., # Extended-variable probabilistic computing with probabilistic d-dimensional bits

Dataset DOI: [10.5061/dryad.sxksn03gd](10.5061/dryad.sxksn03gd)

## Description of the data and file structure

Files were generated that represent individual probabilistic problems (generate✱.py), which were then simulated using various simulator scripts (✱.cpp). A probabilistic Ising machine application-specific integrated circuit was specified using Verilog (rtl/✱.v) alongside look-up tables (rtl/✱.mem), and controlled using C code (✱.c) that ran on an included RISC-V CPU. Verilog (rtlFPGA/✱.v) code using look-up tables (dataFPGA/✱.txt) was also used as an integer programming probabilistic Ising machine. The same problem was run using GAMS (gamsSolvers/✱) as a comparison.

### Files and variables

#### File: Extended_P_Computing_Data.zip

**Description:** Compressed file of all included data and code

#### File: data/✱.txt

**Description:** Human-readable format describing various linear programming pr...,