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 P 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 ≈ 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.
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 P 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 ≈ 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.
Abstract We benchmark classical, simulated-quantum, hybrid, and direct quantum-annealing workflows on a structured binary control problem formulated as a quadratic unconstrained binary optimization (QUBO) model. The benchmark is motivated by greenhouse heater scheduling, where the horizon (H) denotes the number of hourly binary control decisions, but the focus is on solver behavior for a physically decoded control-QUBO formulation. For the main one-day instance ((H=24)), all solver outputs are decoded back into heater schedules and evaluated using the same simulator-side objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid binary quadratic model workflow is less reliable and does not outperform the classical baselines under 15--60 s requested time limits. Direct D-Wave quantum processing unit execution on reduced instances remains feasible in all runs and recovers the exact optimum for (H=10) and (H=12), but the exact-hit rate decreases with increasing horizon. The results do not indicate quantum advantage, but provide a reproducible benchmark for evaluating annealing-based natural and quantum computing workflows on structured control QUBOs. MSC Classification: 90C27 , 90C59 , 81P68 , 93C55
We benchmark current annealing-based optimization workflows on a greenhouse-inspired quadratic unconstrained binary optimization problem for binary heater scheduling, where the horizon H denotes the number of hourly control decisions. For the main one-day instance (H=24), all solver outputs are decoded back into heater schedules and evaluated in the original greenhouse simulator using the same physical objective and feasibility criterion. Classical simulated annealing and path-integral simulated quantum annealing produce feasible near-optimal solutions in all repetitions, with best objectives close to the exact optimum. In contrast, the tested D-Wave Leap Hybrid BQM workflow is less reliable and does not outperform the classical baselines under 15--60~s requested time limits. Direct D-Wave QPU execution on reduced instances remains feasible in all runs and recovers the exact optimum for H=10 and H=12, but the exact-hit rate drops from 5/10 to 2/10 and then to 0/10 at H=14, with substantially higher variance than the classical baselines. The results do not indicate quantum advantage, but provide a reproducible, physically decoded benchmark that exposes the current strengths and limitations of classical, hybrid, and direct quantum annealing workflows on structured control QUBOs.
We introduce VeloxQ, a fast solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to many real-world optimization tasks. Unlike approaches that depend on emerging quantum hardware, VeloxQ can be deployed on conventional computing infrastructure. We benchmark VeloxQ against state-of-the-art QUBO solvers from several families. These include quantum annealers, specifically D-Wave's Advantage and Advantage2 platforms; the digital-quantum BF-DCQO algorithm for Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum; physics-inspired algorithms including Simulated Bifurcation, Parallel Annealing, and tropical tensor networks; and conventional methods including CPLEX, brute force, BEIT's Chimera solver, and Branch-and-Bound variants. The benchmark suite covers native quantum-annealer topologies, embedded all-to-all instances, HUBO-derived instances, planted-solution instances, certified-solver regimes, and dense Branch-and-Bound test cases. Across the benchmark suite, VeloxQ delivers competitive solution quality and runtime, and in several regimes outperforms the compared solvers. VeloxQ also demonstrates strong scalability. Among the solvers considered in this study, it was the only method we could run on the largest sparse instances within our computational budget, including problems with up to 108 sparsely connected variables. These findings position VeloxQ as a competitive and practical tool for tackling large-scale QUBO/HUBO problems, offering a practical alternative to existing quantum and classical optimization methods.
Quadratic Unconstrained Binary Optimization (QUBO) provides a versatile framework for representing NP-hard combinatorial problems, yet existing solvers often face trade-offs among speed, accuracy, and scalability. In this work, we introduce a quantum-inspired solver (QIS) that unites branch-and-bound pruning, continuous gradient-descent refinement, and quantum-inspired heuristics within a fully adaptive control architecture. We benchmark QIS3 against eight state-of-the-art solvers, including genetic algorithms, coherent Ising machines, simulated bifurcation, parallel tempering, simulated annealing, our prior QIS2 version, D-Wave's simulated-annealing (Neal), and Gurobi on three canonical QUBO problem classes: Max-Cut, NAE-3SAT, and Sherrington-Kirkpatrick spin glass problems. Under a uniform runtime budget, QIS3 attains the best solution on nearly all instances, achieving optimality in 94% of max-cut instances. These results establish QIS3 as a robust, high-performance solver that bridges classical exact strategies and quantum-inspired heuristics for scalable QUBO optimization.
Abstract As interest in quantum and related optimization paradigms continues to grow, fairly and systematically comparing their performance across practical problem settings remains challenging. This challenge arises because these approaches often target different problem classes, use different mathematical representations, and are affected differently by modeling choices. As a result, observed performance depends not only on the solver itself, but also on how a problem is formulated, reformulated, and translated into a solver-specific input language. This work presents a publicly available and extensible benchmarking framework that unifies advances in quantum, quantum-hybrid, quantum-inspired, and classical optimization by enabling consistent comparison across use cases, solvers, and models. We address the diversity of solver “languages”—from mixed-integer programming (MIP) formulations for branch-and-bound methods over quadratic unconstrained binary optimization (QUBO) models for quantum annealers to constrained quadratic models (CQM) for hybrid approaches — as well as the influence of modeling choices, such as binary encodings and penalty formulations, on both performance and solution fidelity. By supporting systematic variation across the three dimensions of use case, solver, and model, the framework reveals trade-offs that single-dimension benchmarks overlook, clarifies when native formulations are preferable, and enables rigorous evaluation of practical combinatorial optimization problems. The two case studies, vehicle routing and maximum cut, illustrate this principle: their contrasting outcomes show that the effectiveness of a solver depends strongly on how well the chosen model representation matches the solver backend and the use case.
Large-scale combinatorial scheduling problems -- job-shop scheduling, flow-shop scheduling, and vehicle routing among them -- remain NP-hard at practically relevant scale, and quantum computing has entered this space along two related tracks: genuinely quantum solvers, principally quantum annealers and gate-based devices running the quantum approximate optimization algorithm (QAOA), and quantum-inspired classical solvers, such as coherent Ising machines and digital annealers, that borrow the same Ising/QUBO problem structure without requiring quantum hardware. This article synthesizes both tracks as applied specifically to scheduling. We trace the theoretical foundations from quantum and simulated annealing through the QUBO formulation techniques that make scheduling problems solver-ready, then review direct applications to job-shop, flow-shop, and vehicle-routing problems, reporting the concrete, verified numbers the underlying studies provide. The consistent finding is that quantum hardware remains constrained by qubit connectivity, embedding overhead, and shallow achievable circuit depth to small benchmark instances, while quantum-inspired classical solvers, unconstrained by qubit count, already reach scheduling-relevant problem sizes with reported performance competitive with or exceeding classical heuristics. We close by identifying benchmarking rigor, hardware connectivity, and the near-total absence of work on dynamic, online scheduling as the field's clearest open problems.