Operator learning for efficient quantum computation
Abstract
An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a framework that maps discrete operators onto compact, structured quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary --dense or sparse-- operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems --such as quantum simulation and quantum chemistry-- and achieve improved resource scaling in comparison to standard Suzuki--Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator --relevant for solving partial differential equations-- while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. These results motivate the extension of the framework to a broader class of operator-synthesis problems beyond the prototypical engineering and quantum applications considered here.
Versions
Related
- Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation
- Efficient quantum Gibbs sampling of stabilizer codes using hybrid computation
- Finite attainment and efficient computation of regularized quantum channel relative entropy
- Variational Perturbation Theory in Open Quantum Systems for Efficient Steady State Computation
- Bayesian bilevel operator learning with low-rank adaptation for efficient uncertainty quantification of PDE inverse problems.
BibTeX
@misc{over2026operator,
title = {{Operator learning for efficient quantum computation}},
author = {Paul Over and Sergio Bengoechea and Leonardo Borello Busilacchi and Martin Kiffner and Thomas Rung and Alexios A. Michailidis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.20184},
eprint = {2606.20184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.20184},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operator learning for efficient quantum computation
AU - Paul Over
AU - Sergio Bengoechea
AU - Leonardo Borello Busilacchi
AU - Martin Kiffner
AU - Thomas Rung
AU - Alexios A. Michailidis
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.20184
UR - https://arxiv.org/abs/2606.20184
AB - An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a framework that maps discrete operators onto compact, structured quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary --dense or sparse-- operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems --such as quantum simulation and quantum chemistry-- and achieve improved resource scaling in comparison to standard Suzuki--Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator --relevant for solving partial differential equations-- while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. These results motivate the extension of the framework to a broader class of operator-synthesis problems beyond the prototypical engineering and quantum applications considered here.
ER -