QiHD implements Quantum-Inspired Hamiltonian Descent (QIHD), a quantum-inspired, GPU-enabled solver framework for mixed-integer quadratic programming (MIQP).

QIHD generates candidate solutions through Hamiltonian-descent dynamics and can optionally refine them with a classical local optimizer. The current solver pipeline is:

MIQP / QUBO / BoxQP / LCQP problem -> QIHD backend -> optional refiner -> Response

QiHD is the successor to OpenPhiSolve, originally developed by Artephi Computing. This repository keeps the original BSD 3-Clause license attribution while continuing development under PhysOpt.

The Python package namespace has changed from phisolve to qihd. The primary solver class is now MIQPSolver; the old PhiMIQP name remains available as a compatibility alias.

See MIGRATION.md for details.

MIQP is a classic optimization model characterized by a quadratic objective function defined over a feasible region with both continuous and binary variables:

pip install qihd

For CUDA 12 JAX support:

pip install "qihd[cuda12]"

For local development:

git clone https://github.com/PhysOpt/QiHD.git
cd QiHD
pip install -e .

import numpy as np

from qihd import MIQP, MIQPSolver, QIHD, PDQP

Q = np.array([[2.0, -1.0], [-1.0, 2.0]])
w = np.array([-1.0, -1.0])

problem = MIQP(Q=Q, w=w, n_binary_vars=2)
backend = QIHD(n_shots=100, n_steps=1000, seed=0)
refiner = PDQP()

solver = MIQPSolver(problem, backend=backend, refiner=refiner)
result = solver.solve()

print(result.minimum())
print(result.minimizer)

• qihd.problems contains MIQP, QUBO, BoxQP, and LCQP problem classes.
• QIHD is the quantum-inspired Hamiltonian descent backend.
• qihd.refiners contains classical refiners such as PDQP; additional refiners live in the same subpackage.
• MIQPSolver orchestrates problem compilation, sample generation, refinement, and response construction.
• Response stores samples, objective values, timing details, and solution helpers.

Existing code using PhiMIQP can continue to work during the migration window:

from qihd import PhiMIQP

The recommended new import is:

from qihd import MIQPSolver

QiHD is derived from OpenPhiSolve. See NOTICE and LICENSE for attribution and license details.

If you use QiHD or Quantum-Inspired Hamiltonian Descent in your work, please cite:

@misc{chaudhary2025quantum,
  title = {Quantum-Inspired Hamiltonian Descent for Mixed-Integer Quadratic Programming},
  author = {Chaudhary, Shreya and Cheng, Jinglei and Kushnir, Samuel and Leng, Jiaqi and Liu, Pengyu and Peng, Yuxiang and Wang, Hanrui and Wu, Xiaodi},
  year = {2025},
  howpublished = {Poster presented at the NeurIPS Workshop on GPU-Accelerated and Scalable Optimization},
  note = {Workshop poster}
}

For questions, issues, and contributions, please use the GitHub issue tracker.