We propose a practical, physics-inspired benchmarking suite to challenge both quantum and classical computers by mapping real-time quantum dynamics to a common optimization format. Using a parallel-in-time encoding, we convert the real-time propagator of an $n$-qubit, possibly non-Hermitian, Hamiltonian into quadratic unconstrained binary optimization (QUBO) instances that are executable in a solver-agnostic manner on quantum annealers and classical optimizers alike. This enables direct, like-for-like performance comparisons across fundamentally different computational paradigms. To stress-test the framework, we consider eight representative dynamical models spanning single-qubit rotations, multiqubit entangling gates (Bell, Greenberger-Horne-Zeilinger, cluster), and $\mathcal{P}\mathcal{T}$-symmetric and other non-Hermitian generators, and evaluate success probability and time to solution as standard benchmarking metrics. Applying this method to two generations of D-Wave quantum annealers and to state-of-the-art classical solvers (simulated annealing and the graphics-processing unit–accelerated VeloxQ), we find that Advantage2 consistently outperforms its predecessor, while VeloxQ retains the shortest absolute run-times, reflecting the maturity of classical heuristics. We further extend the benchmarks to large-scale instances ($N\approx {10}^5$), establishing a demanding classical baseline for future hardware. Together, these results position the parallel-in-time QUBO framework as a versatile and physically motivated test bed for quantitatively tracking progress toward quantum-competitive simulation of dynamical systems.

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• Adiabatic quantum optimization
• Quantum benchmarking
• Quantum computation
• Quantum information theory
• Quantum information with solid state qubits
• Quantum simulation
• Dynamical systems
• Simulated annealing