Norm-Aware Product Formulas for Hamiltonian Simulations
Abstract
With the target of efficiently solving the quantum-mechanical Schrödinger equation on future quantum computers, first- and second-order product formulas for the time-evolution operator are proposed, designed to exploit hierarchies in the operator norms of the individual Hamiltonian components. Inspired by the THRIFT product formula, these decomposition schemes achieve a suppression of the leading error term by a factor of alpha<1 with respect to the standard Lie--Trotter--Suzuki splitting of the same order, where alpha quantifies the norm ratio between the dominant and subdominant parts of the Hamiltonian. Unlike THRIFT, the proposed formulas retain the general product-formula structure, making them applicable to Hamiltonians whose terms act on an arbitrary number of qubits. The advantages of this approach are demonstrated through numerical experiments on engineered two-dimensional spin-1/2 XY model systems and isolated molecules within the double-factorization framework.
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BibTeX
@misc{moreno2026normaware,
title = {{Norm-Aware Product Formulas for Hamiltonian Simulations}},
author = {Carlos A. Piñeiro Moreno and Pascal Krause and Annika Bande},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31070},
eprint = {2610.31070},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31070},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Norm-Aware Product Formulas for Hamiltonian Simulations
AU - Carlos A. Piñeiro Moreno
AU - Pascal Krause
AU - Annika Bande
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31070
UR - https://arxiv.org/abs/2610.31070
AB - With the target of efficiently solving the quantum-mechanical Schrödinger equation on future quantum computers, first- and second-order product formulas for the time-evolution operator are proposed, designed to exploit hierarchies in the operator norms of the individual Hamiltonian components. Inspired by the THRIFT product formula, these decomposition schemes achieve a suppression of the leading error term by a factor of alpha<1 with respect to the standard Lie--Trotter--Suzuki splitting of the same order, where alpha quantifies the norm ratio between the dominant and subdominant parts of the Hamiltonian. Unlike THRIFT, the proposed formulas retain the general product-formula structure, making them applicable to Hamiltonians whose terms act on an arbitrary number of qubits. The advantages of this approach are demonstrated through numerical experiments on engineered two-dimensional spin-1/2 XY model systems and isolated molecules within the double-factorization framework.
ER -