The problems with binary optimization without quadratic limitations (QUBO) represent important challenges in areas ranging from machine learning to materials science, but finding the truly optimal solution remains difficult. Zedonpen from Purdue University, Daniel Dellu from Carnegie Mellon University and Google, and David E. Vernal Neyra from Purdue University, are now demonstrating a new approach that combines the strengths of both quantum and classical computing. Their team developed a hybrid algorithm that integrates quantum solvers that guide heuristics within the classic branch and binding framework, providing a practical pathway towards a guaranteed optimal solution. By carefully deciding when and where quantum computation should be used and optimizing the structure of the problem for quantum processing, they achieve significant improvements in solution time and computational effort, outperforming the performance of key commercial optimization software in a wide range of benchmark problems. This work establishes the possibilities of hybrid quantum classical strategies that will bring significant advances in accurate optimization for complex real-world challenges.
It details a variety of approaches, including classical algorithms, quantum algorithms such as quantum annealing and variational Quantum algorithms, and hybrid methods. Core focus is to solve problems expressed as Qubos or ISING models. This is a versatile formulation of many computationally challenging problems such as Maxcut and graph coloring. The key theme is robust benchmarking and evaluation methods to compare the performance of both classic and quantum solvers.
Classical approaches frequently employ methods such as simulation annealing, taboo search, genetic algorithms, and multi-stage strategies. Branching and binding algorithms often combined with truncated planes have been emphasized to be effective in finding the most optimal solution, particularly for sparse problems, with recent work focusing on improving efficiency through techniques such as digitized counter-antibody quantum optimization. The quantum approach uses devices like D-Wave to make quantum annealing stand out by using devices like Qove. Issues include embedding the problem into hardware and verifying the quality of the solution.
Variational quantum algorithms (VQAs), such as the quantum approximate optimization algorithm (QAOA), exist with concerns about the locality of barren plateaus and cost functions, but are investigated as potential solutions. Important trends include combining quantum and classical techniques. For example, quantum algorithms are used to generate candidate solutions for classical branches and bound algorithms. The problem structure greatly affects solver performance, and scalability remains a major hurdle for both classic and quantum methods. The current study highlights addressing challenges such as barren plateaus of VQAS and effective embedding for quantum annealing. This framework integrates Ising Solvers as heuristics within classic B and B algorithms to preserve global optimality assurances. This work presents a practical implementation, investigates the strategic applications of ISING solvers within the B and B search trees, and optimizes the QUBO embedding process. Scientists meticulously evaluated this method on hundreds of Qubo instances sourced from Qubolib. JL employs both the commercial solvers Gurobi and the D-Wave Quantum Annealer as comparative benchmarks and heuristic tools within the B and B framework.
Co-Inovation is located in custom branching rules designed to improve Qubo Embedding, effectively derive B and B searches and reduces calculation efforts. The experiments systematically compared the performance of this hybrid approach with the default Grubi setting, measuring both the survey time and the number of nodes during the search. The results show a significant improvement in efficiency. The hybrid method has investigated nodes up to 11% less solution times and 17% less than standard Grubi optimization. This improvement comes from the strategic integration of ISING solvers, effectively pruning the search space and directing B and B algorithms towards the optimal solution. This work presents a practical implementation published as open source software and benchmarks a suite of over 5,000 Qubo instances. The team investigated strategies for strategically applying ISING solvers during the B and B search process and introduced custom branching rules optimized for QUBO embedding. The experiments show that the median reduction in the number of nodes investigated with the B and B algorithm was 17%, and overall solution time was reduced by 11% compared to standard Grubi Solver.
Specifically, the geometric mean shifted by a 10-s shift (SGM10) reduced the baseline resolution time from 154 seconds to 137 seconds. This method incorporates a preprocessing step that reduces the size of sub-problems and uses branching rules that are informed by the extent of the variables in the qubo interaction graph. This hybrid approach leverages the strengths of both classic and ISING-based solvers to allow for more efficient investigation of the solution space while maintaining guarantees of global optimum. The team has successfully interfaced algorithms with both simulated and hardware ISING solvers, demonstrating the versatility and potential to tackle complex optimization challenges. The researchers have developed practical, openly available implementations to systematically investigate when and how to utilize these solvers to optimize the use of the optimization process, along with branching rules designed specifically for Qubo Embedding. Extensive testing of over 5,800 instances from the Qubolib collection demonstrates the effectiveness of this method. The results show that incorporating the solution from the ISING solver improves performance by about 5%, with optimized branching rules alone, with solution times and number of nodes investigated exceeding 10%.
However, the team acknowledges that the observed improvements are currently not attaining the theoretical maximum that can be achieved through the full integration of solvers. Future research will focus on developing more effective methods for integrating quantum solvers as per node heuristics to further enhance the functionality of this hybrid strategy. This work examines the possibility of combining classical and quantum techniques to accelerate the precise solver of structured Qubo problems.
