D-Wave's Nonlinear-Program Hybrid Solver: Description and Performance Analysis
Eneko Osaba, Pablo Miranda-Rodriguez
TL;DR
This paper introduces D-Wave's Nonlinear-Program Hybrid Solver (NL-Hybrid) as a new member of the Hybrid Solver Service (HSS) portfolio. NL-Hybrid supports nonlinear inequalities/equalities and novel variable types (e.g., permutation, subset) beyond traditional binary encodings, enabling efficient modeling of complex problems. Through a benchmark of 45 instances across TSP, KP, and MCP, NL-Hybrid generally outperforms BQM-Hybrid and CQM-Hybrid on TSP and KP, while showing limited advantage on MCP where binary formulations fare better. The work demonstrates NL-Hybrid's potential to broaden the reach of quantum-classical hybrids for industrially relevant problems, while also identifying latency and problem-encoding limitations that guide future research and formulations.
Abstract
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.