Faster matrix product state preparation by exploiting symmetry-induced block-sparsity
Abstract
Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have U(1)-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of √2. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.
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BibTeX
@misc{rupprecht2026faster,
title = {{Faster matrix product state preparation by exploiting symmetry-induced block-sparsity}},
author = {Felix Rupprecht and Sabine Wölk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28489},
eprint = {2605.28489},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28489},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Faster matrix product state preparation by exploiting symmetry-induced block-sparsity
AU - Felix Rupprecht
AU - Sabine Wölk
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2605.28489
UR - https://arxiv.org/abs/2605.28489
AB - Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have U(1)-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of √2. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.
ER -