Meta-Analytics, Inc.

A World Leader in Solving QUBO and Related Combinatorial Optimization Problems

The QUBO Model:

The Quadratic Unconstrained Binary Optimization (QUBO) problem is notable for:

  • Its ability to serve as a unifying framework for many disparate classical optimization models
  • Its role as the primary application focus of the quantum computing community

Mathematical Formulation:

The formal definition of the QUBO is:

               Maximize or Minimize 

Where x is a vector of binary decision variables and Q is a symmetric matrix of problem data.


QUBO models are important in practice because:

  • Most combinatorial optimization problems can easily be re-formulated, by using quadratic penalties to replace classical constraints, into the form of a QUBO model.
  • This re-casting takes a wide variety of classically formulated models, with their own unique structures, and creates equivalent models with the common structure of the QUBO model.
  • Thus, the QUBO model represents an alternative approach for modeling and solving combinatorial optimization problems.

Our QUBO Solver:

AlphaQUBO, our solver for QUBO models:

  • Is a world leading, state-of-the-art metaheuristic procedure for solving the general QUBO model
  • We are currently solving problems of size up to 1,000,000 variables
  • Research and development efforts are underway leading to even larger applications.
  • Extensive computational experience confirms high quality performance
    • Regardless of problem density or other characteristics
    • Superior performance compared to other QUBO solvers, including those from the quantum community.


Applications of the QUBO model for solving important problems have been reported in such diverse areas as:

  •  Financial Services
  •  Transportation
  •  Manufacturing
  •  Pharmaceuticals
  •  Network and Energy Systems
  •  Machine learning
  •  Many others

Our Services:

We serve the optimization community by:

  • Offering advanced solvers for QUBO models, currently available through Amazon Web Services
  • Offering consulting services pertaining to important problems in industry and government with a special focus on applications that can be modeled and solved as QUBO or QUBO related models.