Quantum annealing applications, challenges and limitations for optimisation problems compared to classical solvers

TL;DR

The paper assesses the practicality of quantum annealing for optimization by benchmarking D-Wave's hybrid Leap solvers against classical solvers (CPLEX, Gurobi, IPOPT) across BLP, BQP, and MILP tasks, including a real-world unit-commitment problem. It treats problems as QUBOs with penalty terms for constraints, leveraging the Ising/QUBO mapping $F(oldsymbol{x}) = ext{Obj}(oldsymbol{x},Q) + \sum_k ext{λ_k} P_k(oldsymbol{x})^2$ and the adiabatic framework to evolve from $H_I$ to $H_F$, with the Pegasus-based hardware (5760 qubits) and hybrid decomposition enabling larger instances. The main findings show strongest performance for BQP, where the hybrid solver provides consistent optimal solutions faster than classical solvers in some regimes; for BLP, D-Wave matches optimal values but scaling and time penalties erode benefits; for quadratic constraints, improvements exist but are not reliably optimal; MILP unit commitment remains outside the solver’s advantage, even on reduced instances. Overall, the work delineates the current boundaries of quantum annealing in industry-scale optimization, underscores the importance of problem encoding, embedding, and parameter tuning, and points to hardware/topology advances (e.g., Zephyr) as critical for future practicality.

Abstract

Quantum computing is rapidly advancing, harnessing the power of qubits' superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a hybrid workflow between classical and quantum computing instances, D-Wave has succeeded in pushing this boundary to the realm of industrial use. Furthermore, they have recently opened up to mixed integer linear programming (MILP) problems, expanding their applicability to many relevant problems in the field of optimisation. However, the extent of their suitability for diverse problem categories and their computational advantages remains unclear. This study conducts a comprehensive examination by applying a selection of diverse case studies to benchmark the performance of D-Wave's hybrid solver against that of industry-leading solvers such as CPLEX, Gurobi, and IPOPT. The findings indicate that D-Wave's hybrid solver is currently most advantageous for integer quadratic objective functions and shows potential for quadratic constraints. To illustrate this, we applied it to a real-world energy problem, specifically the MILP unit commitment problem. While D-Wave can solve such problems, its performance has not yet matched that of its classical counterparts.

Figures (8)

• Figure 1: Mean objective function value and computational time comparison between CPLEX, Gurobi, IPOPT and D-Wave's hybrid solver for the BLP with a single linear constraint. The results are averaged over 5 runs and the minimum and maximum deviation from the mean value is shown by the vertical lines.
• Figure 2: Mean objective function value (a) and computational time (b) comparison between CPLEX, Gurobi, IPOPT and D-Wave's hybrid solver for the BLP with increasingly more constraints. The results are averaged over 5 runs and the minimum and maximum deviation from the mean value is shown by the vertical lines.
• Figure 3: Mean objective function value (top) and computational time (bottom) comparison between two classical solvers and D-Wave's hybrid solver for the BLP with a single quadratic constraint. In (a) the complexity scales with the number of variables. In (b), the variables are fixed to 500, whereas the complexity scales with increasing $C$ as stated in \ref{['eq:c1']}. All results are averaged over 5 runs, and the vertical lines show the minimum and maximum deviation from the mean value. Gurobi's solve time is significantly larger than all other solvers and is thereby excluded here for visibility.
• Figure 4: Comparison of the objective function value (a) and computational time (b) between D-Wave and the previously introduced classical solvers for BQP with 500 binary variables. The results are averaged over 5 runs. The run time is limited to 1000s, resulting in CPLEX not finding the optimal solution for increasing $C$.
• Figure 5: Mean relative difference of D-Wave's hybrid solution and those supplied by CPLEX and IPOPT for the BQP. The vertical lines indicate the difference between CPLEX's and IPOPT's mean solution to the maximum and minimum solution provided by D-Wave within all 5 runs.