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  • Open Access

Optimal symbolic construction of matrix product operators and tree tensor network operators

Hazar Çakır1,*, Richard M. Milbradt1,†, and Christian B. Mendl1,2,‡

  • *Contact author: hazar.cakir@tum.de
  • †Contact author: r.milbradt@tum.de
  • ‡Contact author: christian.mendl@tum.de
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Phys. Rev. B 112, 035101 – Published 1 July, 2025

DOI: https://doi.org/10.1103/8993-8xn5

Abstract

This research introduces an improved framework for constructing matrix product operators and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic “sum of operator strings” form that can be translated into a tensor network structure. Combining the existing bipartite-graph-based approach and a newly introduced symbolic Gaussian elimination preprocessing step, our proposed method improves upon earlier algorithms in cases when Hamiltonian terms share the same prefactors. We test the performance of our method against established ones for benchmarking purposes. Finally, we apply our methodology to the model of a cavity filled with molecules in a solvent. This open quantum system is cast into the hierarchical equation of motion setting to obtain an effective Hamiltonian. Construction of the corresponding TTNO demonstrates a sublinear increase of the maximum bond dimension.

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Phys. Rev. B 112, 035101– Published 1 July, 2025
  • Received 20 March 2025
  • Accepted 10 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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