Cross-Platform Benchmarking of Near-Term Quantum Optimisation Algorithms

TL;DR

This work introduces a cross-platform benchmarking framework for near-term quantum optimization applied to a dense QUBO derived from defective graphene configurations. It benchmarks gate-based VQE on IBM QPUs and quantum annealing on D-Wave QCaaS against classical solvers up to $72$ variables, analyzing embedding, noise, and runtime overheads. Key contributions include a reproducible methodology with hardware- and algorithm-agnostic metrics (e.g., optimal-solution probability $P_s$ and approximation ratio AR) and detailed scaling analyses that reveal polynomial scaling for simulated annealing and provisional polynomial scaling for quantum annealing, alongside clear limitations for current VQE hardware. The findings suggest that, for these benchmarks, classical annealing remains competitive or superior in both solution quality and runtime, while the framework provides a solid basis for fair comparisons and guiding future hardware and algorithm improvements in optimization tasks.

Abstract

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum optimisation algorithms using a dense Quadratic Unconstrained Binary Optimisation (QUBO) materials science problem as a representative test-case. To solve this problem, we implement two methods, the Variational Quantum Eigensolver (VQE) and Quantum Annealing (QA), on commercially-available gate-based and quantum annealing devices that are accessible via Quantum-Computing-as-a-Service (QCaaS) models. To analyse the performance of these algorithms, we use a toolbox of relevant metrics and compare performance against three classical algorithms. We employ quantum methods to solve fully-connected QUBOs of up to $72$ variables, and find that algorithm performance beyond this is restricted by device connectivity, noise and classical computation time overheads. The applicability of our approach goes beyond the selected configurational analysis test-case, and we anticipate that our approach will be of use for optimisation problems in general.

Figures (22)

• Figure 1: An example of one of the graphene structures explored in this work: a $3\times3$ supercell (which corresponds to an $18 \times 18$ QUBO matrix), where the grey spheres represent carbon atoms. The unit cell is shown in the inset. There is no vacancy in this example. Periodic boundary conditions apply, making this structure a $3$-regular graph (note: the graph that corresponds to the QUBO matrix is fully connected after adding constraints).
• Figure 2: Visual representation of the methods used in this work, as described in the main text.
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