Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications

Jiace Sun; Lixue Cheng; Shi-Xin Zhang

doi:10.22331/q-2025-06-24-1782

Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications

Jiace Sun¹, Lixue Cheng^1,2, and Shi-Xin Zhang³

¹Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
²Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (SAR) 999077, China
³Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Published:	2025-06-24, volume 9, page 1782
Editor:	Marco Cerezo
Eprint:	arXiv:2403.08441v4
Doi:	https://doi.org/10.22331/q-2025-06-24-1782
Citation:	Quantum 9, 1782 (2025).

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Abstract

Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply stabilizer states to tackle quantum many-body ground state problems and introduce the concept of stabilizer ground states. We establish an equivalence formalism for identifying stabilizer ground states of general Pauli Hamiltonians. Moreover, we develop an exact and linear-scaled algorithm to obtain stabilizer ground states of 1D local Hamiltonians and thus free from discrete optimization. This proposed equivalence formalism and linear-scaled algorithm are not only applicable to finite-size systems, but also adaptable to infinite periodic systems. The scalability and efficiency of the algorithms are numerically benchmarked on different Hamiltonians. Finally, we demonstrate that stabilizer ground states are promising tools for not only qualitative understanding of quantum systems, but also cornerstones of more advanced classical or quantum algorithms.

Featured image: The exact stabilizer ground state of a given 1D local Hamiltonian can be found in linear time by sequentially constructing state machines located on subsystems.

Popular summary

Stabilizer states represent a unique category of quantum states featured by their simple mathematical structure. Compared with most of the quantum states whose descriptions require exponentially scaled classical resources, stabilizer states can be classically represented with polynomial-scaled resources. Due to their classical representability and abilities to capture long-range entanglements, they have been commonly used in quantum information, quantum error corrections, and simulating quantum circuits.

In this work, we expanded the application of stabilizer states to tackle quantum many-body problems, a challenging area due to the exponential growth of the Hilbert space dimension. We introduced the concept of stabilizer ground states and developed both theoretical formalisms and efficient algorithms to find stabilizer ground states of different types of Hamiltonians, including both finite systems and infinite periodic Hamiltonians. We demonstrate that stabilizer ground states are promising tools for not only qualitative understanding of quantum systems, but also cornerstones of more advanced classical or quantum algorithms.

This work offers a fresh perspective on quantum many-body problems, showcasing the broader applicability of stabilizer states by bridging quantum many-body physics with the quantum information toolbox. This work could be fundamental in developing novel tools for studying many-body physics problems.

► BibTeX data

@article{Sun2025stabilizerground,
  doi = {10.22331/q-2025-06-24-1782},
  url = {https://doi.org/10.22331/q-2025-06-24-1782},
  title = {Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications},
  author = {Sun, Jiace and Cheng, Lixue and Zhang, Shi-Xin},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1782},
  month = jun,
  year = {2025}
}

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[2] Davide Castaldo and Markus Reiher, "Utility-Scale Quantum Computational Chemistry", The Journal of Physical Chemistry Letters 17 29, 8140 (2026).

[3] Abhinav Anand and Kenneth R. Brown, "Stabilizer configuration interaction: Finding molecular subspaces with error detection properties", Physical Review A 112 3, 032421 (2025).

[4] Caroline E. P. Robin, "Stabilizer-accelerated quantum many-body ground-state estimation", Physical Review A 112 5, 052408 (2025).

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[7] Xiangjian Qian, Jiale Huang, and Mingpu Qin, "Augmenting Density Matrix Renormalization Group with Clifford Circuits", Physical Review Letters 133 19, 190402 (2024).

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[9] Andi Gu, Salvatore F. E. Oliviero, and Lorenzo Leone, "Doped stabilizer states in many-body physics and where to find them", Physical Review A 110 6, 062427 (2024).

[10] Caroline E. P. Robin and Martin J. Savage, "Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology", arXiv:2604.26376, (2026).

[11] Fen Zuo, "Improving stabilizer approximation with quantum strategy", arXiv:2412.06320, (2024).

[12] James W. T. Keeble, Alessandro Lovato, and Caroline E. P. Robin, "Neural Quantum States in Non-Stabilizer Regimes: Benchmarks with Atomic Nuclei", arXiv:2603.28646, (2026).

[13] Davide Castaldo and Markus Reiher, "Utility-scale quantum computational chemistry", arXiv:2603.19081, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-08 03:36:39) and SAO/NASA ADS (last updated successfully 2026-08-08 03:36:40). The list may be incomplete as not all publishers provide suitable and complete citation data.

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