Quantum Hamiltonian Evolution for Coherent Quantum Learning
Abstract
We introduce Coherent Quantum Learning (CQL), a training framework for quantum learning models in which the model parameters are quantum degrees of freedom evolved under a Hamiltonian that encodes the loss function. Current quantum machine learning retains classical optimization: parameters are updated by a classical outer loop using gradient estimates from measurements, and quantum coherence has no role in the training dynamics, just as in any classical treatment of the same problem. In the quantum case, a parameter register initialized in superposition evolves unitarily, and probability amplitude concentrates near low-loss configurations through interference, without gradient computation or classical feedback. We give an explicit construction using block encodings and Hamiltonian simulation, applicable to arbitrary parameterized circuits. Numerical experiments on binary classification and interferometric phase estimation confirm that the evolved distribution peaks at the optimal parameters, matching gradient-based performance. The construction is compatible in principle with fault-tolerant implementations and extends to batched training via sequential Hamiltonian evolution.
Related
- Quantum Sensing and Hamiltonian Learning under Stochastic Parameter Evolution
- Quantum Evolution Networks Learn Long-Time Coherent Dynamics in Driven Spin Registers
- Comment on "Supervised Learning with Quantum Hamiltonian Embeddings" (arXiv:2610.26833)
- Supervised Learning with Quantum Hamiltonian Embeddings
- Full-Trajectory Learning of Open Quantum Systems: Dynamical Emulation and the Limits of Hamiltonian Identifiability
BibTeX
@misc{acedo2026quantum,
title = {{Quantum Hamiltonian Evolution for Coherent Quantum Learning}},
author = {Ignacio B. Acedo and Javier Gonzalez-Conde and Pablo Rodriguez-Grasa and Barry C. Sanders and Lirandë Pira},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03640},
eprint = {2609.03640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03640},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Hamiltonian Evolution for Coherent Quantum Learning
AU - Ignacio B. Acedo
AU - Javier Gonzalez-Conde
AU - Pablo Rodriguez-Grasa
AU - Barry C. Sanders
AU - Lirandë Pira
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03640
UR - https://arxiv.org/abs/2609.03640
AB - We introduce Coherent Quantum Learning (CQL), a training framework for quantum learning models in which the model parameters are quantum degrees of freedom evolved under a Hamiltonian that encodes the loss function. Current quantum machine learning retains classical optimization: parameters are updated by a classical outer loop using gradient estimates from measurements, and quantum coherence has no role in the training dynamics, just as in any classical treatment of the same problem. In the quantum case, a parameter register initialized in superposition evolves unitarily, and probability amplitude concentrates near low-loss configurations through interference, without gradient computation or classical feedback. We give an explicit construction using block encodings and Hamiltonian simulation, applicable to arbitrary parameterized circuits. Numerical experiments on binary classification and interferometric phase estimation confirm that the evolved distribution peaks at the optimal parameters, matching gradient-based performance. The construction is compatible in principle with fault-tolerant implementations and extends to batched training via sequential Hamiltonian evolution.
ER -