Researchers Ernesto Acosta and Carlos Cano of the University of Granada, together with Guillermo Botella of Complutense University of Madrid, have reformulated the parameter-optimization problem of variational quantum algorithms as a Quadratic Unconstrained Binary Optimization problem, the native language of quantum annealers. Their work, published as volume 8, article 101 of the journal, demonstrates that the same machines designed to find low-energy configurations of combinatorial optimization problems can also serve as scalable optimizers for gate-based quantum models, opening a hybrid pathway that combines gate-model quantum computing, quantum annealing, and classical control in a single training loop.

The core insight behind the method is elegant. Variational quantum algorithms depend on a Hamiltonian expressed in terms of trainable rotation angles, and the exponential structure of the circuit’s unitary operator can be transformed, through a heuristic substitution that replaces imaginary phases with real-valued angles, into sums of real exponential terms. Those terms map naturally onto the quadratic binary cost functions that quantum annealers minimize. In other words, the mathematical structure of the ansatz itself provides the bridge: instead of estimating gradients with hundreds of circuit shots, the team encodes candidate parameter regions directly into QUBO form and asks the annealer to find the configuration with the lowest energy.

Because continuous rotation angles must be represented with discrete binary variables, the researchers developed a recursive refinement strategy that progressively narrows the search space. The parameter range is partitioned into segments, validation points are sampled within each partition, and the QUBO problem is solved to identify the most promising regions. The angle range is then rescaled — in their worked example, halved at each level — and centered on the best solution found so far, and the process repeats. This coarse-to-fine scheme approximates high-quality continuous solutions with a small number of discrete QUBO solves, trading resolution for tractability in a controlled way.

A key strength of the framework is its adaptability. The method exposes a rich set of configurable metaheuristic parameters, including the number of training levels, the number of partitions per angle, and the number of validation points per partition. These knobs allow practitioners to tune the balance between solution quality and computational cost according to the problem at hand and the computational resources available. The authors also integrate an adaptive metaheuristic optimization scheme rather than a fixed search rule, making the training procedure generalizable to arbitrary Hamiltonians rather than being tied to a specific circuit family or ansatz design.

To test the approach, the team benchmarked their adiabatic training scheme on publicly available classification datasets, including the Iris, Heart Disease, and Diabetes datasets from the UCI machine learning repository. The experimental evaluations show that the method achieves accuracy comparable to, and in some configurations better than, established classical and evolutionary optimizers, while significantly reducing computational overhead. The authors’ hyperparameter exploration reveals that the highest performance efficiency — accuracy gained per unit of training time — tends to occur at lower numbers of levels and partitions, meaning that modest configurations already capture most of the benefit before costs escalate.

The implications extend beyond raw benchmark numbers. Gradient-based training on near-term quantum hardware is plagued by noisy gradient estimates, since every partial derivative must be inferred from finite numbers of noisy circuit measurements. Meanwhile, barren plateaus, whose origins have been linked both to deep random circuits and to noise accumulation, can render gradients exponentially vanishing and classical optimizers effectively blind. A gradient-free, annealer-driven optimizer sidesteps both pathologies: it never estimates a derivative, and its search is driven by the energy landscape of the QUBO encoding rather than by local slope information that may not exist in any meaningful sense.

The study builds on a growing body of work connecting annealing-style hardware to machine learning. Previous research has shown that QUBO formulations can be used to train classical machine learning models, that Ising machines can serve as training engines for standard neural networks, and that universal adiabatic quantum computers can be harnessed for neural network training. An earlier preprint by the same team had already explored adiabatic training for variational quantum algorithms; the new journal publication consolidates that line of inquiry into a general, configurable framework with systematic experimental validation, code released through a public repository, and full experimental detail across multiple datasets and hyperparameter regimes.

What emerges is a compelling vision of near-term quantum computing as a genuinely hybrid enterprise. In the architecture the Granada and Madrid researchers describe, a gate-based quantum processor executes the variational circuit, a quantum annealer solves the training problem at each iteration, and a classical system orchestrates the recursive refinement and manages the workflow. Each platform contributes what it does best, and none has to shoulder the full burden alone. As annealing hardware scales and QUBO encodings grow more expressive, this division of labor could become a practical route to training quantum models that classical optimizers struggle to handle.

Challenges certainly remain. The heuristic substitution that enables real-valued QUBO encoding sacrifices strict unitarity, and the discretization of continuous parameters means solution precision depends on the depth of the refinement schedule. The authors’ own data show that pushing training levels and partitions higher does not always pay off, underscoring the need for careful configuration. Still, the demonstration that quantum annealers can train variational quantum algorithms with competitive quality and lower overhead marks a meaningful step. For a field hunting for any advantage in the noisy intermediate-scale era, recruiting one quantum machine to train another may prove to be one of the more inventive entries in the playbook.

Subject of Research: A QUBO-based method that uses quantum annealers to train variational quantum algorithms without gradients.

Article Title: QUBO-based training for VQAs on quantum annealers

Article References: Acosta, E., Botella, G., & Cano, C. (2026). QUBO-based training for VQAs on quantum annealers. Quantum Machine Intelligence, 8(2), Article 101. https://doi.org/10.1007/s42484-026-00441-1

Image Credits: AI Generated

DOI: 10.1007/s42484-026-00441-1

Keywords: quantum computing, variational quantum algorithms, quantum annealing, QUBO, optimization, barren plateaus, quantum machine learning, hybrid quantum computing, metaheuristics, NISQ era, gradient-free training, Hamiltonians