Observable-targeted variational quantum simulation of Hamiltonian dynamics
Abstract
Standard variational quantum simulation seeks to reproduce the evolution of the full quantum state, although many applications require only the expectation values of a few observables. We study a variational method for pure-state Hamiltonian dynamics that updates circuit parameters to reproduce the evolution of selected expectation values. An exact error identity guides the choice of observables, motivating a construction based on repeated commutators of the target with the Hamiltonian. For Pauli observables and Pauli-rotation circuits, the update can be estimated without ancillary qubits or controlled operations for overlap estimation. Across six- and ten-qubit spin, fermionic, and molecular benchmarks, the observable-targeted update extends the median time within the target-error tolerance compared with standard variational quantum simulation with equal shot budgets. These results show that directing the variational update toward the target observable can extend accurate simulation without increasing the measurement cost per time step.
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BibTeX
@misc{zambrano2026observabletargeted,
title = {{Observable-targeted variational quantum simulation of Hamiltonian dynamics}},
author = {Leonardo Zambrano and Luciano Pereira and Antonio Acín},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.24794},
eprint = {2609.24794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24794},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Observable-targeted variational quantum simulation of Hamiltonian dynamics
AU - Leonardo Zambrano
AU - Luciano Pereira
AU - Antonio Acín
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.24794
UR - https://arxiv.org/abs/2609.24794
AB - Standard variational quantum simulation seeks to reproduce the evolution of the full quantum state, although many applications require only the expectation values of a few observables. We study a variational method for pure-state Hamiltonian dynamics that updates circuit parameters to reproduce the evolution of selected expectation values. An exact error identity guides the choice of observables, motivating a construction based on repeated commutators of the target with the Hamiltonian. For Pauli observables and Pauli-rotation circuits, the update can be estimated without ancillary qubits or controlled operations for overlap estimation. Across six- and ten-qubit spin, fermionic, and molecular benchmarks, the observable-targeted update extends the median time within the target-error tolerance compared with standard variational quantum simulation with equal shot budgets. These results show that directing the variational update toward the target observable can extend accurate simulation without increasing the measurement cost per time step.
ER -