QUBO++ (C++) Documentation

Getting Started

  1. HUBO and QUBO
  2. Quick Start
  3. Installation and License Management

Basics

This section provides a step-by-step introduction to QUBO++. By reading the pages in order, you will learn how to define variables and expressions, model optimization problems, and solve them using QUBO++. After completing this tutorial, you should be able to use QUBO++ for most typical applications.

  1. Defining Variables and Creating Expressions
  2. Solving Expressions
  3. Array of Variables and Array Functions
  4. Solving Partitioning Problem Using Array of Variables
  5. Permutation Matrix and Solving Assignment Problem
  6. Integer Variables and Solving Simultaneous Equations
  7. Factorization Through HUBO Expression
  8. Range Constraints and Solving Integer Linear Programming

Topics

This section provides topic-wise explanations of selected features of QUBO++. Each page focuses on a specific topic and offers deeper insights into design decisions, usage patterns, and, where appropriate, internal implementations. This section is not intended to be exhaustive, but to complement the Tutorial and Reference sections by providing a deeper understanding of QUBO++.

  1. Data Types of Variables and Expressions
  2. Basic Operators and Functions
  3. Basic Operators and Functions for Arrays
  4. Multi-dimensional Integers, Variables, and Expressions
  5. Comparison Operators
  6. Expression Classes
  7. Evaluating Expressions
  8. Replace functions
  9. Negated Literals
  10. Sum Functions for Multi-dimensional Arrays
  11. Einsum Function for Tensor Contraction
  12. Slice and Concat Functions
  13. One-Hot to Integer Conversion
  14. Easy Solver Usage
  15. Exhaustive Solver Usage
  16. ABS3 Solver Usage
  17. Gurobi Optimizer Usage
  18. Search Parameters
  19. Performance Tips

Case Studies

This section provides examples of solving optimization, mathematical, and graph problems using QUBO++. See the Case Studies page for the full list.

Quick References

  1. Variables and Expressions
  2. Operators and Functions for Expressions
  3. Operations and Functions for Integer Variables and Constraints
  4. Solutions

Back to top

Page last modified: 2026.05.13.