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arXiv:2601.08085 · Physical Review Research

Learning parameter curves in feedback-based quantum optimization algorithms

Vicente Peña Pérez, Matthew D. Grace, Christian Arenz, Alicia B. Magann

quant-phSubmitted Jan 13, 2026• Announced Jan 14, 2026• 0 citations
v1 · Jan 13, 2026v2 · Oct 1, 2026
arXivHTMLPDF

Abstract

Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling cost associated with these measurements can be significant. Here, we ask whether FQA parameter sequences can be predicted using classical machine learning, obviating the need for qubit measurements altogether. To this end, we train a teacher-student model to map a MaxCut problem instance to an associated FQA parameter curve in a single classical inference step. Numerical experiments show that this model can accurately predict FQA parameter curves across a range of problem sizes, including problem sizes not seen during model training. To evaluate performance, we compare the predicted parameter curves in simulation against FQA reference curves and linear quantum annealing schedules. We observe similar results to the former and performance improvements over the latter. These results suggest that machine learning can offer a heuristic, practical path to reducing sampling costs and resource overheads in quantum algorithms.

Journal reference
Physical Review Research 8, 033378 (2026)
DOI
10.1103/pgbz-zm8h
Comments
13 pages, 6 figures. To be submitted to Physical Review Research Journal

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The Feedback-based Algorithm for Quantum Optimization (FALQON) offers a deterministic alternative to variational quantum algorithms by bypassing classical optimization loops. However, maintaining convergence on large problem instances often requires restricting the time step, necessitating quantum circuit depths that exceed Noisy Intermediate-Scale Quantum (NISQ) hardware capabilities. This paper investigates the parameter transferability of second-order FALQON applied to the Max-Cut problem on 3-regular graphs. Through numerical experiments evaluating quantum circuits up to 16 layers on graphs up to 24 nodes, we demonstrate a highly advantageous scaling behavior: transferring feedback parameters optimized on small instances to larger target graphs yields significantly higher approximation ratios than natively optimizing the parameters directly on the larger graphs. This performance advantage arises because parameters trained on smaller instances can safely adopt aggressively larger time steps. By offloading the expensive parameter discovery phase to small-scale instances, this transfer strategy simultaneously reduces computational overhead and enhances the approximation ratio, thereby bringing FALQON closer to practical viability on near-term quantum architectures.
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