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QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent

Samuel Kushnir, Jiaqi Leng, Yuxiang Peng, Lei Fan, Xiaodi Wu

TL;DR

QHDOPT introduces an open-source framework that enables nonlinear, box-constrained optimization on near-term quantum devices via the Quantum Hamiltonian Descent (QHD) algorithm. It leverages Hamiltonian-oriented programming (HOP) and the SimuQ stack to provide hardware-agnostic problem embedding, automatic differentiation, and a hybrid quantum-classical workflow that includes decoding and classical refinement. The paper demonstrates two concrete examples (QP and nonlinear exponential problems), benchmarks against classical solvers, and shows that quantum-assisted initialization combined with fast classical refiners can outperform purely classical approaches within current hardware limits. The work highlights the current frontier of quantum optimization software, addresses a gap in continuous optimization tooling, and outlines practical paths for expanding device support, problem classes, and global-optimality guarantees in future work.

Abstract

We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to various supported quantum backends (i.e., quantum hardware machines). These features enable users, even those without prior knowledge or experience in quantum computing, to utilize the power of existing quantum devices for nonlinear and nonconvex optimization tasks. In its intermediate compilation layer, QHDOPT employs SimuQ, an efficient interface for Hamiltonian-oriented programming, to facilitate multiple algorithmic specifications and ensure compatible cross-hardware deployment. The detailed documentation of QHDOPT is available at https://github.com/jiaqileng/QHDOPT.

QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent

TL;DR

QHDOPT introduces an open-source framework that enables nonlinear, box-constrained optimization on near-term quantum devices via the Quantum Hamiltonian Descent (QHD) algorithm. It leverages Hamiltonian-oriented programming (HOP) and the SimuQ stack to provide hardware-agnostic problem embedding, automatic differentiation, and a hybrid quantum-classical workflow that includes decoding and classical refinement. The paper demonstrates two concrete examples (QP and nonlinear exponential problems), benchmarks against classical solvers, and shows that quantum-assisted initialization combined with fast classical refiners can outperform purely classical approaches within current hardware limits. The work highlights the current frontier of quantum optimization software, addresses a gap in continuous optimization tooling, and outlines practical paths for expanding device support, problem classes, and global-optimality guarantees in future work.

Abstract

We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to various supported quantum backends (i.e., quantum hardware machines). These features enable users, even those without prior knowledge or experience in quantum computing, to utilize the power of existing quantum devices for nonlinear and nonconvex optimization tasks. In its intermediate compilation layer, QHDOPT employs SimuQ, an efficient interface for Hamiltonian-oriented programming, to facilitate multiple algorithmic specifications and ensure compatible cross-hardware deployment. The detailed documentation of QHDOPT is available at https://github.com/jiaqileng/QHDOPT.
Paper Structure (37 sections, 21 equations, 7 figures, 6 tables)

This paper contains 37 sections, 21 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Organization.
  3. Problem formulation: box-constrained nonlinear optimization
  4. Solving problems in QHDOPT
  5. Pre-processing and problem encoding.
  6. Deployment and decoding.
  7. Classical refinement.
  8. Unique design features
  9. Hamiltonian-oriented programming (HOP).
  10. Multi-backend compatibility.
  11. Automatic differentiation.
  12. Quantum Hamiltonian Descent
  13. Mathematical formulation and interpretation
  14. Real-machine implementation
  15. The Workflow of QHDOPT
  16. ...and 22 more sections

Figures (7)

  • Figure 1: An Overview of QHDOPT. A. Building the stack of quantum computing for nonlinear optimization. B. The workflow of QHDOPT, inspired by the Hamiltonian-oriented programming paradigm.
  • Figure 2: Input formats in QHDOPT. QHDOPT supports both symbolic and numerical input formats.
  • Figure 3: Deploying and executing QHD on the D-Wave quantum computer
  • Figure 4: Bitstring-to-vector decoder in QHDOPT
  • Figure 5: Solving a quadratic programming problem using QHDOPT
  • ...and 2 more figures

Theorems & Definitions (3)

  • Example 1: Box-constrained Quadratic programming
  • Example 2: Spherical constraints
  • Example 3: One-hot embedding for $x_1x_2$