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

QUBO++ is a framework for formulating and solving combinatorial optimization problems as polynomials of binary variables (QUBO/HUBO). Declaring constraints explicitly with cons() lets the bundled solvers search efficiently for solutions that satisfy them.

  • C++ and Python — Use QUBO++ from C++ (QUBO++) or Python (PyQBPP).
  • Easy installation — sudo apt install qbpp for C++, pip install pyqbpp for Python. No build from source required.
  • Symbolic DSL — Write optimization models as mathematical expressions, not matrix indices. Use natural for-loops to build constraints, or leverage vector operations for loop-free formulations.
  • Native constraints — Wrap a constraint in cons() to declare it: the constraint is treated specially, and the bundled solvers search efficiently for solutions that satisfy it. This reduces the burden of penalty-weight tuning, and the same declarations are treated as hard constraints by the exact and MIP solvers. See Native Constraints (Python version) for details.
  • Unlimited-degree HUBO — Supports high-order terms of any degree, not just quadratic. Native support for negated literals (~x) avoids the term explosion caused by replacing $\overline{x}$ with $1-x$.
  • Massive variable capacity — A single model can use up to 2,147,483,647 ($2^{31}-1$) binary variables.
  • Arbitrary-precision integer coefficients — Handles integer coefficients of unlimited bit width. No overflow worries, from 32-bit to thousands of digits.
  • Real (double) coefficients — Besides integers, coefficients can be double. Expressions are built in double and automatically quantized to the integer solver when solved, with the energy returned as a double — so you work entirely in real numbers without dealing with the integer backend.
  • Three built-in solvers — Easy Solver (fast heuristic), Exhaustive Solver (complete search with optimality guarantee), and ABS3 (GPU+CPU heuristic).
  • GPU-accelerated solving — The built-in ABS3 solver fully utilizes GPU resources for parallel search, with multi-GPU scaling. The Exhaustive Solver also automatically uses CUDA GPUs when available.
  • CPU parallel acceleration — All solvers run multithreaded on multicore CPUs.
  • Experimental third-party solver support — Call Gurobi, SCIP, HiGHS, GLPK, CBC, IBM CPLEX, IBM Qiskit Optimization, dimod ExactSolver, Fixstars Amplify, D-Wave Ocean (Advantage / native QPU / Leap Hybrid / Neal / Tabu / Steepest), OpenJij, TYTAN-SDK MIKAS, qubovert, Simulated Bifurcation, and Google OR-Tools CP-SAT through a unified Solver.search() protocol. Gurobi, SCIP, HiGHS, GLPK, and CBC are available from C++ (QUBO++) as well; the others are available from PyQBPP. See QUBO/HUBO Solvers, MILP Solvers, and CP Solvers.
  • Run anywhere — From a Raspberry Pi to a laptop, GPU servers, and supercomputers. Available for amd64 (x86_64) and arm64 Linux.

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: Parallel search on multicore CPUs.
  • Unlimited integer coefficients: Supports integer coefficients of arbitrary magnitude.

Exhaustive Solver

  • Enumerates all solutions to QUBO/HUBO formulations on multicore CPUs and CUDA GPUs.
  • Optimality guaranteed: the global optimum is found and certifiable.
  • Multithreaded acceleration: Parallel search on multicore CPUs.
  • Unlimited integer coefficients: Supports integer coefficients of arbitrary magnitude.
  • GPU acceleration: If a CUDA GPU is available, GPU workers automatically join the search alongside CPU threads. GPU acceleration is available for coefficients up to 128-bit integers; larger coefficients fall back to CPU-only search.

ABS3 Solver

  • Heuristic solver on multicore CPUs and CUDA GPUs: Searches for solutions to QUBO/HUBO instances using both CPU threads and CUDA GPUs.
  • Unlimited integer coefficients: Supports integer coefficients of arbitrary magnitude.
  • Multi-GPU scaling: Uses all detected GPUs on a Linux host. GPU acceleration is available for coefficients up to 128-bit integers; larger coefficients fall back to CPU-only search.

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.

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

QUBO++ Licensing

A free Trial license (30 days, 10,000 variables) is available via the QUBO++ User Portal. After installing QUBO++, run qbpp-license -s to obtain today’s sign-up code, then register at the portal to receive your Trial key.

For details on license activation, license types, and terms, see License Management.

Third-Party Libraries

The following libraries are linked into the QUBO++ shared objects (qbpp_*.so):

Optional Solver Backends

Besides the three built-in solvers, QUBO++ can hand a model to a number of external solvers, grouped by the model form each one consumes:

  • QUBO/HUBO Solvers — the model is taken directly (Gurobi, D-Wave, Fixstars Amplify, OpenJij, IBM CPLEX, …).
  • MILP Solvers — the QUBO is linearized into a pure MILP first (SCIP, HiGHS, GLPK, CBC).
  • CP Solvers — constraint programming (Google OR-Tools CP-SAT).

Each backend must be installed separately and ships under its own license (some require a commercial or academic license). These integrations are experimental — their APIs may change without notice. See each page above for the full solver list, installation, and per-backend caveats.

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Page last modified: 2026.07.12.