QUBO++: A model-and-solve framework for combinatorial optimization via QUBO/HUBO

• A C++ library for constructing polynomials of binary variables to solve combinatorial optimization problems.
• Currently built for amd64 (x86_64) and arm64 Linux systems.
• Bundled with two CPU solvers: Easy Solver (heuristic) and Exhaustive Solver (complete search).
• Bundled with a GPU solver: ABS3.
• Supports High-Order Unconstrained Binary Optimization (HUBO) of degree up to 16.
• Multithreading acceleration is applied using oneTBB wherever possible.
• Includes APIs for calling the Gurobi Optimizer to solve Quadratic Unconstrained Binary Optimization (QUBO) problems.
• Copyright: © 2026 Koji Nakano. All rights reserved.

QUBO++ Solvers: Easy Solver, Exhaustive Solver, ABS3 Solver

Easy Solver

• Heuristic solver optimized for QUBO/HUBO: Searches for solutions to QUBO/HUBO models on multicore CPUs.
• Multithreaded acceleration: Uses Intel oneTBB for parallel search.
• Unlimited integer coefficients: Supports integer coefficients of arbitrary magnitude.

Exhaustive Solver

• Enumerates all solutions to QUBO/HUBO formulations on multicore CPUs.
• Optimality guaranteed: the global optimum is found and certifiable.
• Multithreaded acceleration: Uses Intel oneTBB for parallel search.
• Unlimited integer coefficients: Supports integer coefficients of arbitrary magnitude.

ABS3 Solver

• GPU-optimized heuristic solver: Finds solutions to QUBO/HUBO instances on CUDA-enabled GPUs.
• Multi-GPU scaling: Uses all detected GPUs on a Linux host.
• 64-bit integer coefficients: Supports coefficients representable in signed 64-bit integers.

ABS3 Supported GPU architectures

• sm_80 : NVIDIA A100 (Ampere)
• sm_86 : NVIDIA RTX A6000, GeForce RTX 3090/3080/3070 (Ampere)
• sm_89 : NVIDIA RTX 6000 Ada, GeForce RTX 4090/4080/4070 (Ada)
• sm_90 : NVIDIA H100 / H200 / GH200 (Hopper)
• sm_100 : NVIDIA B200 / GB200 (Blackwell, data center)
• sm_120 : GeForce RTX 5090/5080/5070(Ti)/5060(Ti)/5050、RTX PRO 6000/5000/4500/4000/2000 Blackwell (workstation)
• Note on verification : Only a subset of the architectures above has been verified on real hardware.

Numeric types

• 32-bit and 64-bit term coefficients
• 64-bit energy values

Performance note

• Arithmetic overflow checks are omitted to maximize performance.

Build Environment

The following environment was used to build QUBO++. QUBO++ is not limited to Ubuntu 20.04; it has also been tested on Ubuntu 22.04/24.04 and other Linux distributions (including CentOS/RHEL-based systems). To ensure compatibility, please use the same or newer versions of the listed components.

• Operating System: Ubuntu 20.04.6 LTS
• C++ Standard: C++17
• glibc: 2.31
• Compiler: g++ 9.4.0
• Boost: 1.81.0
• CUDA: 12.8

oneTBB / TBB dependency

QUBO++ does not bundle TBB. We include TBB headers in public APIs, but the library itself does not require linking against TBB for the default use cases.

• Build & run verified on: Ubuntu 20.04 (classic TBB 2020.1), 22.04 / 24.04 (oneTBB 2021+).

Directory Structure and Key Files

• bin/ - Executable
  • qbpp-license: QUBO++ License manager
• include/ — Header files
  • qbpp.hpp: Main QUBO++ BQ Edition toolkit
  • qbpp_abs3_solver.hpp: ABS3 GPU Solver
  • qbpp_defs.hpp: Common definitions and macros
  • qbpp_easy_solver.hpp: Easy Solver implementation
  • qbpp_exhaustive_solver.hpp: Exhaustive Solver implementation
  • qbpp_grb.hpp: Gurobi Optimizer interface
  • qbpp_misc.hpp: Miscellaneous library
• lib/ — QUBO++ shared libraries
  • libqbpp.so: Shared library for the QUBO++ core
  • libqbpp_abs3c32.so: Shared library for the ABS3 GPU solver with 32-bit term coefficients
  • libqbpp_abs3c64.so: Shared library for the ABS3 GPU solver with 64-bit term coefficients
• samples/ — Sample programs
  • factorization.cpp: Integer factorization
  • graph_color.cpp: Graph coloring
  • tsp.cpp: Solving Traveling Salesman Problem using Easy Solver
  • qbpp_tsp.hpp: Creating QUBO model for the TSP
  • integer_poly.cpp: Integer polynomial optimization
  • labs.cpp: Low Autocorrelation Binary Sequences problem
  • nqueen_easy.cpp: Solving N-Queens problem using Easy Solver
  • qbpp_nqueen.hpp: Generates QUBO expression for the N-Queens problem
  • shift_scheduling.cpp: Shift scheduling problem
  • factorization_abs3.cpp: Integer factorization using ABS3
  • labs_abs3.cpp: Low Autocorrelation Binary Sequences problem using ABS3 GPU solver
  • ilp_grb.cpp: Integer Linear Programming example using Gurobi Optimizer

QUBO++ Licensing

License Types

QUBO++ uses Cryptlex for license management. When activating a node-locked license, some information about the execution environment is securely stored on Cryptlex servers to verify the license.

• Anonymous Trial
  • No license key required
  • Valid for 7 days
  • Maximum variable count: 1,000 (CPU) / 1,000 (GPU)
• Registered Trial
  • Requires a free license key
  • Valid for 30 days
  • Maximum variable count: 10,000 (CPU) / 10,000 (GPU)
• Standard License
  • Requires a paid license key
  • Valid for the duration of the license agreement
  • Maximum variable count: 2,147,483,647 ($2^{31} - 1$) (CPU) / 1,000 (GPU)
  • Practically, the maximum variable count may be limited by available physical memory.
• Professional License
  • Requires a paid license key
  • Valid for the duration of the license agreement
  • Maximum variable count: 2,147,483,647 ($2^{31} - 1$) (CPU) / 2,147,483,647 ($2^{31} - 1$) (GPU)
  • Practically, the maximum variable count may be limited by available physical memory.
• Fallback (No license / Expired license)
  • Maximum variable count: 100 (CPU) / 100 (GPU)

Display/Activate/Deactivate QUBO++ License

• The qbpp-license utility (in the /bin directory of the QUBO++ installation) displays, activates, and deactivates the license on the current machine.
• A QUBO++ license must be activated on the machine before QUBO++ programs can run. Otherwise, QUBO++ runs in Fallback Mode.
• Each license key has limits on the number of activations and deactivations. These limits are tracked per license.

Display License

If a license has already been activated on this machine, running qbpp-license displays the current license details (e.g., expiry date/time, activation usage/limit, and license message).

• Registered Trial/Standard License/Professional License You can specify the license key either by environment variable or by command-line option.
  • Using environment variable:

    $ export QBPP_LICENSE_KEY=XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX
    $ qbpp-license
    

  • Using command-line option:

    $ qbpp-license -k XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX
    

• Anonymous Trial
  Just run the command without specifying a license key:

  $ qbpp-license
  

Activate License

• To activate the license on the current machine, add the -a (or --activate) option to the above command:

  $ qbpp-license -a
  

• This consumes one activation from the license.
• If the license is already activated on this machine, running the command again does not consume an additional activation for the same license key.

Deactivate License

• To deactivate the license on the current machine, use the -d (or --deactivate) option:

  $ qbpp-license -d
  

• Anonymous Trial cannot be deactivated.
• Deactivation will increase the deactivation count and free up an activation slot so that the license can be activated again on this or another machine.

Executing QUBO++ with a license key

• For Anonymous Trial, there is no license key to set.
• If you have a license key, specify it in one of the following ways before running your program:
  • Via Code:

    qbpp::license_key("XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX");
    

  • Via Environment Variable:

    export QBPP_LICENSE_KEY=XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX-XXXXXX
    

Notes on the license-check mechanism

• qbpp-license tries to refresh the license status from the license server, so it may take a few seconds depending on your network.
• By default, QUBO++ user programs verify the license using the local cache and do not block on server synchronization. They may contact the license server only when necessary (for example, when the license has not been synchronized for a long time).
• Depending on your network environment, license synchronization by qbpp-license may time out and return an error. In such cases, you can increase the timeout with the -t option:

  $ qbpp-license -t 60
  

  This sets the timeout to 60 seconds.

Terms and Conditions

By using QUBO++, you agree to the following terms and conditions:

1. License Scope
   QUBO++ is provided under a time-limited license, depending on the license type (Anonymous Trial, Registered Trial, Standard or Professional License).

2. Restrictions on Trial Licenses
   The Anonymous Trial and Registered Trial licenses are provided strictly for evaluation purposes only.

3. Standard/Professional Licenses and Payment Requirement
   Standard/Professional Licenses require the purchase of a paid license key. These licenses grant full access to QUBO++ for commercial and research use, subject to the terms of the license agreement.

4. Redistribution
   Redistribution of QUBO++ (in whole or in part, including headers and binaries) is prohibited without prior written permission from the copyright holder.

5. Reverse Engineering
   You may not reverse engineer, decompile, or disassemble any part of the software.

6. Disclaimer
   QUBO++ is provided “as is,” without any warranties, express or implied. The authors shall not be held liable for any damages resulting from the use of this software.

7. Ownership
   All intellectual property rights related to QUBO++ remain the property of the original author or copyright holder.

8. Termination
   This license will automatically terminate if you fail to comply with these terms. Upon termination, you must cease all use of the software and destroy all copies.

Third-Party Libraries

• oneTBB (oneAPI Threading Building Blocks)
  • Licensed under the Apache License 2.0.
  • Copyright © Intel Corporation.
  • See https://www.apache.org/licenses/LICENSE-2.0 for details.
• Boost C++ Libraries
  • Licensed under the Boost Software License, Version 1.0.
  • See https://www.boost.org/LICENSE_1_0.txt for details.
• xxHash
  • Licensed under the BSD 2-Clause License.
  • Copyright © Yann Collet.
  • See https://opensource.org/license/bsd-2-clause/ for details.
• Gurobi Optimizer
  • QUBO++ supporting APIs for integration with the Gurobi Optimizer.
  • To use these APIs, you must obtain a valid license for the Gurobi Optimizer from Gurobi Optimization, LLC.
  • The Gurobi Optimizer is not included with QUBO++, and its use is subject to the terms and conditions of its own license agreement.

If you have any questions regarding licensing or wish to obtain a license key, please contact the distributor or the developer.