# D-Wave's Nonlinear-Program Hybrid Solver: Description and Performance Analysis

arXiv: https://arxiv.org/abs/2410.07980 · HTML: https://mlsanity.com/paper/2410.07980/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 80 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2007.00017/) (2020)
- [Portfolio Optimisation Using the D-Wave Quantum Annealer](https://mlsanity.com/paper/2012.01121/) (2020)
- [Hybrid Approach for Solving Real-World Bin Packing Problem Instances Using Quantum Annealers](https://mlsanity.com/paper/2303.01977/) (2023)
- [Solving a Real-World Package Delivery Routing Problem Using Quantum Annealers](https://mlsanity.com/paper/2403.15114/) (2024)
- [Hybrid Quantum Computing -- Tabu Search Algorithm for Partitioning Problems: preliminary study on the Traveling Salesman Problem](https://mlsanity.com/paper/2012.04984/) (2020)
- [Quantum Annealing for Vehicle Routing Problem with weighted Segment](https://mlsanity.com/paper/2203.13469/) (2022)
- [Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers](https://mlsanity.com/paper/2406.14792/) (2024)
- [Focusing on the Hybrid Quantum Computing -- Tabu Search Algorithm: new results on the Asymmetric Salesman Problem](https://mlsanity.com/paper/2102.05919/) (2021)
- [Hybrid classical-quantum computing: are we forgetting the classical part in the binomial?](https://mlsanity.com/paper/2308.10513/) (2023)
- [QOPTLib: a Quantum Computing Oriented Benchmark for Combinatorial Optimization Problems](https://mlsanity.com/paper/2404.15852/) (2024)
- [Power network optimization: a quantum approach](https://mlsanity.com/paper/2212.01625/) (2022)
- [Solving Logistic-Oriented Bin Packing Problems Through a Hybrid Quantum-Classical Approach](https://mlsanity.com/paper/2308.02787/) (2023)
- [Optimizing decision making for soccer line-up by a quantum annealer](https://mlsanity.com/paper/2112.13668/) (2021)
- [Optimization of Image Acquisition for Earth Observation Satellites via Quantum Computing](https://mlsanity.com/paper/2307.14419/) (2023)
- [Exploring Utility in a Real-World Warehouse Optimization Problem: Formulation Based on Quantum Annealers and Preliminary Results](https://mlsanity.com/paper/2409.09706/) (2024)

## Built on by (most cited first, 5 of 5)

- [Transfer of Knowledge through Reverse Annealing: A Preliminary Analysis of the Benefits and What to Share](https://mlsanity.com/paper/2501.15865/) (2025)
- [Solving Drone Routing Problems with Quantum Computing: A Hybrid Approach Combining Quantum Annealing and Gate-Based Paradigms](https://mlsanity.com/paper/2501.18432/) (2025)
- [Addressing the Minor-Embedding Problem in Quantum Annealing and Evaluating State-of-the-Art Algorithm Performance](https://mlsanity.com/paper/2504.13376/) (2025)
- [Quantum-Assisted Automatic Path-Planning for Robotic Quality Inspection in Industry 4.0](https://mlsanity.com/paper/2507.01462/) (2025)
- [Quantum Annealing for Staff Scheduling in Educational Environments](https://mlsanity.com/paper/2510.12278/) (2025)

## Abstract (arXiv)

The development of advanced quantum-classical algorithms is among the most prominent strategies in quantum computing. Numerous hybrid solvers have been introduced recently. Many of these methods are created ad hoc to address specific use cases. However, several well-established schemes are frequently utilized to address optimization problems. In this context, D-Wave launched the Hybrid Solver Service in 2020, offering a portfolio of methods designed to accelerate time-to-solution for users aiming to optimize performance and operational processes. Recently, a new technique has been added to this portfolio: the Nonlinear-Program Hybrid Solver. This paper describes this solver and evaluates its performance through a benchmark of 45 instances across three combinatorial optimization problems: the Traveling Salesman Problem, the Knapsack Problem, and the Maximum Cut Problem. To facilitate the use of this relatively unexplored solver, we provide details of the implementation used to solve these three optimization problems.