Hardcoding ILP Problems on Physical Ising Machines

Solution Overview

Problem

Physical Ising Machines face limitations in solving Integer Linear Programming (ILP) problems due to the need for embedding ILP into hardware graphs, which is computationally expensive and often results in heuristic solutions with reduced quality and increased running times.

Innovation Solution

A system comprising a classical computer and a physical Ising machine that transforms ILP problems into Quadratic Unconstrained Binary Optimization (QUBO) form, allowing direct hard-coding onto the machine's hardware graph through ClusterForm generation and compilation, enabling efficient and high-quality solutions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If embedding is performed to map ILP problems onto hardware graphs, then the problem can be solved on Physical Ising Machines, but the computational cost increases and solution quality decreases

Engineering Contradiction:

Improvesolution qualityVSAvoidcomputational time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent applies preliminary action by performing variable aggregation and constraint consolidation before the embedding process. The system pre-processes the ILP problem to combine multiple variables into aggregated variables and merge constraints, creating a simplified problem formulation that requires less complex embedding and reduces computational overhead during execution.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent applies segmentation by dividing the ILP problem into independent components that can be processed separately. The system identifies and separates constraints that can be handled independently, allowing each segment to be embedded and solved more efficiently on the hardware graph without requiring complex interconnections for all variables.

Inventive Principle:

Principle #1Segmentation

2Adaptability or versatility

If embedding is performed to map ILP problems onto hardware graphs, then the problem can be solved on Physical Ising Machines, but the device complexity increases

Engineering Contradiction:

Improveproblem solving capabilityVSAvoidembedding complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent applies preliminary action by performing variable aggregation and constraint consolidation before the embedding process. The system pre-processes the ILP problem to combine multiple variables into aggregated variables and merge constraints, creating a simplified problem formulation that requires less complex embedding and reduces computational overhead during execution.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent applies universality by developing a general-purpose variable aggregation framework that can handle different types of ILP problems and constraints. The system uses universal aggregation rules and constraint merging techniques that work across various problem domains, reducing the need for problem-specific embedding complexities.

Inventive Principle:

Principle #6Universality (Multi-functionality)

3Productivity

If heuristic embedding methods are used, then embedding can be performed faster, but solution quality is reduced

Engineering Contradiction:

Improveembedding speedVSAvoidsolution quality

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent applies preliminary action by performing variable aggregation and constraint consolidation before the embedding process. The system pre-processes the ILP problem to combine multiple variables into aggregated variables and merge constraints, creating a simplified problem formulation that requires less complex embedding and reduces computational overhead during execution.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent applies the intermediary principle by introducing aggregated variables as mediators between the original ILP problem and the hardware graph embedding. These aggregated variables serve as intermediate representations that simplify the mapping process while preserving the essential problem structure, enabling both speed and quality.

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS10691771B2System and method to hardcode interger linear optimization problems on physical implementations of the Ising model

Publication Date: 2020.06.23 UNIVERSITIES SPACE RES ASSOC

AI summary

Systems and methods for allowing analog Ising machines to be able to run Integer Linear Programming (“ILP”) problems, i.e. a compilation method for setting the state of the physical memory units, flexible to be adapted to each specific device. The method describes how variables and numeric parameters which specify the problem can be hard-coded (embedded and physically represented) in the hardware circuitry of the device in a deterministic way, with a pre-determined bound on the number of required physical spins to be used in the Ising device.