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The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical Solvers

Pranav Chandarana, Alejandro Gomez Cadavid, Enrique Solano, Thorsten Koch, Stefan Woerner, Narendra N. Hegade

Abstract

We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline--from preprocessing to QPU execution and postprocessing--under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve.

The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical Solvers

Abstract

We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline--from preprocessing to QPU execution and postprocessing--under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve.
Paper Structure (5 sections, 2 equations, 2 figures, 1 table)

This paper contains 5 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Benchmark design and metrics.
  2. Sub-second latency regime.
  3. Time-to-solution distributions.
  4. Sensitivity and interpretation.
  5. Discussion and outlook.

Figures (2)

  • Figure 1: Closeness-to-target $\mathcal{C}(t)$ versus wall-clock time for 3S (left) and 4S (right). Curves show means over 10 instances (point-wise best energy over trials/initialization); shaded bands indicate $\pm 1\sigma$. Vertical dashed line (gray band): HSQC mean runtime $\pm 1\sigma$, $756.9\pm86.2$ ms (3S) and $840.9\pm109.4$ ms (4S). SA/MTS/EasySolve/PT+: 128 vCPUs, AWS; ABS3: $8\times$ A100 GPUs.
  • Figure 2: Per-instance TTS for 3S (top) and 4S (bottom) on a log scale. Each dot represents one instance; horizontal bars mark medians. The hybrid solver (black) occupies a narrow band in both families; SA (blue) and MTS (rose) exhibit substantially wider spread. Failure annotations ($\mathrm{TTS}{=}\infty$) appear above each solver column. The datapoints correspond to the hyperparameters given in Table. \ref{['main:tab:tts_summary']}.