Machine Learning Predicts Feedback-Based Quantum Optimization Parameter Curves for MaxCut Problems

Feedback-based algorithms are increasingly used to optimise complex tasks by iteratively building quantum circuits, yet the repeated measurements of qubits within these algorithms can be computationally expensive. Vicente Peña Pérez, Matthew D. Grace, and Christian Arenz, from Arizona State University and Sandia National Laboratories, alongside Alicia B. Magann, investigate whether classical machine learning can predict the necessary parameters for these algorithms, thereby removing the need for these costly measurements. Their research demonstrates a teacher-student model capable of mapping problem instances to associated algorithm parameter curves with remarkable accuracy. This ability to predict parameter curves extends to problems larger than those used to train the model, offering a potential pathway to significantly reduce resource overheads and accelerate quantum optimisation. The team’s findings suggest machine learning can provide a practical heuristic for enhancing the efficiency of feedback-based quantum algorithms.

Predicting VQE parameters with classical machine learning

Optimise a given task by utilising feedback from qubit measurements to inform the next quantum circuit update. In practice, the sampling cost associated with these measurements can be significant. This research investigates whether Variational Quantum Eigensolver (VQE) parameter sequences can be predicted using classical machine learning, potentially removing the need for qubit measurements. A teacher-student model was trained to map a MaxCut problem instance to an associated VQE parameter curve in a single classical inference step.

Numerical experiments demonstrate that this model accurately predicts VQE parameter curves across a range of problem sizes, including those not used during model training. This approach leverages classical data to accelerate the optimisation process within a quantum algorithm, circumventing the need for repeated quantum sampling and reducing overall computational cost. The findings suggest machine learning can provide a practical heuristic for enhancing the efficiency of feedback-based quantum algorithms.

Predicting FQA Parameters with Machine Learning

The research team developed a novel approach to reduce computational costs in feedback-based quantum algorithms (FQAs) by predicting parameter sequences using classical machine learning. Instead of relying on iterative qubit measurements to refine circuit updates, they designed a teacher-student model to map MaxCut problem instances directly to corresponding FQA parameter curves. This innovative technique bypasses costly qubit sampling, offering a pathway to more efficient quantum computation.

To train this model, the study employed numerical experiments across a range of problem sizes, including instances not used during training, to assess its predictive accuracy. The team compared the predicted parameter curves against both FQA reference curves and conventional linear quantum annealing (QA) schedules, digitised for implementation on circuit-model quantum computers. Results demonstrated that the machine learning model closely tracked the performance of exact FALQON results for parameters rA and φ, consistently exceeding the performance of linear QA schedules for problem sizes n ∈ {8, 10, 12}.

Further investigation tested the model’s generalisation capabilities on larger, previously unseen problem sizes n ∈ {14, 16, 18, 20}, revealing relatively low errors and successful extrapolation of key FALQON parameter curve features. The team generated a training dataset comprising 1,344 instances, derived from exact numerical simulations of FALQON to establish reference parameter curves. Future development could involve training the model to learn a small set of parameters within a parameterized function to enhance scalability. Researchers also propose investigating domain adaptation and meta-learning techniques to improve performance on unseen graph families and broaden the method’s applicability beyond the MaxCut problem.

Machine Learning Predicts Quantum Algorithm Parameters Accurately Scientists

Scientists achieved a breakthrough in reducing computational costs within feedback-based quantum algorithms (FQAs) by successfully predicting parameter sequences using classical machine learning. A teacher-student model was trained to map MaxCut problem instances directly to associated FQA parameter curves, effectively bypassing the need for iterative qubit measurements. Numerical experiments demonstrated the model’s ability to accurately predict these curves across varying problem sizes, including instances not used during training.

This predictive capability opens avenues for substantial resource savings in quantum computation. Experiments revealed that the predicted parameter curves closely mirrored those generated by traditional FQA methods, establishing a high degree of accuracy. Furthermore, tests proved performance improvements when comparing the predicted curves against linear quantum annealing schedules, indicating potential for enhanced efficiency. Data shows a consistent clustering of FALQON parameter curves around a common profile, suggesting inherent predictability.

The core of this work lies in developing a model that predicts the full FQA parameter curve in a single classical inference step, replacing the layer-by-layer qubit measurements typically required. Researchers observed that FALQON parameter curves exhibit a characteristic shape , an initial peak region of rapid variation followed by a stable tail , across diverse MaxCut problem instances. This consistent pattern motivated the development of the machine learning model, which leverages problem features to forecast parameter sequences without running the complete feedback procedure. The study focused on solving MaxCut problems on 19 non-isomorphic, unweighted 3-regular graphs with ten nodes, generating a dataset of FALQON parameter curves for model training and validation. Measurements confirm the model’s ability to generalise to unseen problem instances, demonstrating its robustness and adaptability.

Machine Learning Predicts Quantum Algorithm Performance Curves Recent

This research demonstrates the successful prediction of feedback-based algorithm (FQA) parameter curves using a classical machine learning model. By training a teacher-student model on the MaxCut problem, the authors achieved accurate predictions of parameter curves, even for problem sizes exceeding those used during training. This offers a potential pathway to reduce the computational demands of FQA by replacing iterative qubit measurements with a single, classical inference step.

The significance of this work lies in providing a measurement-free alternative to the standard iterative feedback procedure within FQA. Results indicate that the machine learning-predicted parameter curves closely match reference curves generated by the FQA itself, and also outperform linear scheduling approaches. This suggests a viable method for optimising quantum state preparation and potentially improving performance in digitised quantum annealing settings. The authors acknowledge limitations in the scalability of their approach, noting a performance decrease for problem sizes significantly larger than those used for training.

Future research should focus on extending the model’s capacity to handle increased problem complexity and investigating the relationship between training data requirements and model scalability. Further work could also explore obtaining training data directly from quantum hardware runs, balancing data generation costs against the benefits of a more robust model.