Quantum algorithms & hardware
QHD
Research code for numerical simulations, quantum-device experiments, and benchmarking. QHDOPT provides the end-to-end optimization toolkit.
Quantum optimization
QHDOPT
QHDOPT implements Quantum Hamiltonian Descent (QHD), a quantum extension of gradient descent for nonlinear and nonconvex optimization. Its accessible interface and SimuQ-powered compiler connect optimization problems to quantum hardware. GPU-based Quantum-Inspired Hamiltonian Descent (QIHD) also supports large-scale empirical studies and applications on today's hardware.
Quantum-inspired optimization on GPUs
QIHD · OpenPhiSolve
An open-source GPU implementation of Quantum-Inspired Hamiltonian Descent for mixed-integer quadratic programming.
Key Features
Designed for the optimization community, with no prior quantum computing knowledge required.
Automatic mapping to quantum backends such as D-Wave and IonQ, with GPU-based backends for QIHD.
A built-in compiler powered by SimuQ.
Automatic post-processing and fine-tuning of results.
Support for both gate-based and analog quantum computers.
Research in Action
Precision Oncology workshop and live QIHD demonstration
I am co-organizing Quantum Technologies for Precision Oncology, November 5–6, 2026, in Washington, DC.
We will give a live demonstration of applying QIHD to cancer treatment planning. Scheduled for November 5, the demonstration will show how quantum-inspired optimization can be used in treatment-planning workflows.
Final-stage selection in the NIH Quantum Computing Challenge
Our QHD-based application for accelerating cancer treatment planning in radiation oncology has been selected for the final stage of the NIH Quantum Computing Challenge. NIH named Artephi Computing’s “Accelerating Cancer Treatment Planning using Quantum Computing” among the Stage 2 Milestone 1 winners, advancing to the final hardware-demonstration stage.
QHD provides the theoretical foundation and the target for quantum hardware implementation. QIHD provides a GPU-based proxy for QHD’s performance, while already delivering speedups over commercial software in our treatment-planning work.
Quantum-inspired Hamiltonian descent in finance
A BCG article highlights quantum-inspired Hamiltonian descent for financial portfolio optimization. In a synthetic benchmark of roughly 1,000 portfolio segments, the Hamiltonian-descent method running on CPUs found better risk–return trade-offs than Monte Carlo sampling and often converged in under a minute, compared with tens of minutes to hours for Monte Carlo. These results illustrate a practical financial use of quantum-inspired optimization on existing hardware.
Tutorials & Related Talks
QHDOPT tutorial · TUT 25
A hands-on introduction to optimization with QHDOPT.
Exponential Quantum Speedup in Optimization: Theory and Practice
Hamiltonian-Oriented Quantum Algorithm Design and Programming
Related Publications
Quantum Hamiltonian Descent
Quantum Hamiltonian Descent
A Quantum-Classical Performance Separation in Nonconvex Optimization
A Quantum Central Path Algorithm for Linear Optimization · QIP 2025
Quantum Hamiltonian Descent for Non-smooth Optimization
(Sub)Exponential Quantum Speedup for Optimization
Quantum-Inspired Hamiltonian Descent
Quantum-Inspired Hamiltonian Descent for Mixed-Integer Quadratic Programming. Extended abstract at the ScaleOPT workshop, NeurIPS 2025. The GPU implementation is available as OpenPhiSolve.
Yuxiang Peng presented a progress report on applications in healthcare, communications, and machine learning at INFORMS 2025.
Citation
QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent
If you use QHDOPT in your work, please cite our paper.
Samuel Kushnir, Jiaqi Leng, Yuxiang Peng, Lei Fan, and Xiaodi Wu.
INFORMS Journal on Computing 37(1), 107–124 (2025).
BibTeX
@article{kushnir2025qhdopt,
author = {Kushnir, Samuel and Leng, Jiaqi and Peng, Yuxiang and Fan, Lei and Wu, Xiaodi},
title = {{QHDOPT}: A Software for Nonlinear Optimization with {Quantum Hamiltonian Descent}},
journal = {INFORMS Journal on Computing},
year = {2025},
volume = {37},
number = {1},
pages = {107--124},
doi = {10.1287/ijoc.2024.0587},
url = {https://doi.org/10.1287/ijoc.2024.0587}
}Acknowledgments
QHDOPT's development is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing under Award Number DE-SC0020273, the Air Force Office of Scientific Research under Grant No. FA95502110051, the U.S. National Science Foundation grant CCF-1816695, CCF-1942837 (CAREER), ECCS-2045978, a Sloan research fellowship, the Simons Quantum Postdoctoral Fellowship, a Simons Investigator award through Grant No. 825053, as well as an open-source quantum software grant from the Unitary Fund.