Initial-State Preparation for Strongly Correlated Molecules from Matrix Product States: Benchmarking and Environment-Aware Divide-and-Conquer Compilation
Abstract
Compiling classically optimized matrix product states (MPSs) into quantum circuits is a promising route to initial-state preparation for strongly correlated molecules, but the accuracy, gate cost, and classical scalability of existing MPS compilation methods have not been systematically assessed. Here, we benchmark representative analytical, variational, and hybrid MPS compilation methods for strongly correlated systems including hydrogen chains and iron-sulfur clusters. We compare state infidelity, CNOT gate count, classical runtime, and parallel scalability across different system sizes and bond dimensions. We also introduce a divide-and-conquer environment-aware compilation algorithm (DCE), which optimizes each local isometry approximation according to its contribution to the prepared-state fidelity. The results reveal complementary operating regimes: direct variational compilation methods are gate-efficient for some smaller molecular systems with O(10) qubits and O(10) bond dimensions or moderate accuracy targets with infidelity of order 10−1, whereas divide-and-conquer methods scale more favorably for larger systems and relatively higher bond dimensions of O(10−102), particularly when target infidelities below 10−1 are required. Within the latter family, environment-aware optimization improves accuracy over unitary-distance-based compilation while retaining task-level parallelism. For the FeMo-cofactor (FeMoco), we find the DCE algorithm together with the MPS obtained in the entanglement-minimized orbitals (EMOs) provides a resource-efficient route to initial-state preparation. Our results provide practical guidance for selecting and developing MPS compilation methods for strongly correlated molecular simulations.
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BibTeX
@misc{liu2026initialstate,
title = {{Initial-State Preparation for Strongly Correlated Molecules from Matrix Product States: Benchmarking and Environment-Aware Divide-and-Conquer Compilation}},
author = {Haiqi Liu and Longfei Chang and Zhendong Li and Wei-Hai Fang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33834},
eprint = {2610.33834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33834},
}
RIS
TY - UNPB
TI - Initial-State Preparation for Strongly Correlated Molecules from Matrix Product States: Benchmarking and Environment-Aware Divide-and-Conquer Compilation
AU - Haiqi Liu
AU - Longfei Chang
AU - Zhendong Li
AU - Wei-Hai Fang
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33834
UR - https://arxiv.org/abs/2610.33834
AB - Compiling classically optimized matrix product states (MPSs) into quantum circuits is a promising route to initial-state preparation for strongly correlated molecules, but the accuracy, gate cost, and classical scalability of existing MPS compilation methods have not been systematically assessed. Here, we benchmark representative analytical, variational, and hybrid MPS compilation methods for strongly correlated systems including hydrogen chains and iron-sulfur clusters. We compare state infidelity, CNOT gate count, classical runtime, and parallel scalability across different system sizes and bond dimensions. We also introduce a divide-and-conquer environment-aware compilation algorithm (DCE), which optimizes each local isometry approximation according to its contribution to the prepared-state fidelity. The results reveal complementary operating regimes: direct variational compilation methods are gate-efficient for some smaller molecular systems with O(10) qubits and O(10) bond dimensions or moderate accuracy targets with infidelity of order 10^−1, whereas divide-and-conquer methods scale more favorably for larger systems and relatively higher bond dimensions of O(10−10^2), particularly when target infidelities below 10^−1 are required. Within the latter family, environment-aware optimization improves accuracy over unitary-distance-based compilation while retaining task-level parallelism. For the FeMo-cofactor (FeMoco), we find the DCE algorithm together with the MPS obtained in the entanglement-minimized orbitals (EMOs) provides a resource-efficient route to initial-state preparation. Our results provide practical guidance for selecting and developing MPS compilation methods for strongly correlated molecular simulations.
ER -