Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering

Erenay Karacan; Yanbin Chen; Christian B. Mendl

doi:10.22331/q-2025-02-06-1624

Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering

Erenay Karacan¹, Yanbin Chen¹, and Christian B. Mendl^1,2

¹Technical University of Munich, School of Computation, Information and Technology, Boltzmannstraße 3, 85748 Garching, Germany
²Technical University of Munich, Institute for Advanced Study, Lichtenbergstraße 2a, 85748 Garching, Germany

Published:	2025-02-06, volume 9, page 1624
Editor:	Yu Tong
Eprint:	arXiv:2401.09091v4
Doi:	https://doi.org/10.22331/q-2025-02-06-1624
Citation:	Quantum 9, 1624 (2025).

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Abstract

Hamiltonian simulation is a domain where quantum computers have the potential to outperform their classical counterparts. One of the main challenges of such quantum algorithms is increasing the system size, which is necessary to achieve meaningful quantum advantage. In this work, we present an approach to improve the scalability of eigenspace filtering for the ground state preparation of a given Hamiltonian. Our method aims to tackle limitations introduced by a small spectral gap and high degeneracy of low energy states. It is based on an adaptive sequence of eigenspace filtering through Quantum Eigenvalue Transformation of Unitary Matrices (QETU) combined with spectrum profiling. By combining our proposed algorithm with state-of-the-art phase estimation methods, we achieved good approximations for the ground state energy with local, two-qubit gate depolarizing probability up to $10^{-4}$. To demonstrate the key results in this work, we ran simulations with the transverse-field Ising Model on classical computers using $\texttt{Qiskit}$. We compare the performance of our approach with the static implementation of QETU and show that we can consistently achieve three to four orders of magnitude improvement in the absolute error rate.

Featured image: We propose to better the performance of eigenspace filtering through an intermediary spectrum profiling. This alleviates the challenges posed by small spectral gap, in practice. Our spectral profiling estimates the range of occupied states depending on the initial state and helps us to encode a "stretched" Hamiltonian in the state preparation circuit.

► BibTeX data

@article{Karacan2025enhancing,
  doi = {10.22331/q-2025-02-06-1624},
  url = {https://doi.org/10.22331/q-2025-02-06-1624},
  title = {Enhancing {S}calability of {Q}uantum {E}igenvalue {T}ransformation of {U}nitary {M}atrices for {G}round {S}tate {P}reparation through {A}daptive {F}iner {F}iltering},
  author = {Karacan, Erenay and Chen, Yanbin and Mendl, Christian B.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1624},
  month = feb,
  year = {2025}
}

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Cited by

[1] Erenay Karacan, "Phase estimation with compressed controlled time evolution", Physical Review A 113 4, 042420 (2026).

[2] Erenay Karacan, Conor Mc Keever, Michael Foss-Feig, David Hayes, and Michael Lubasch, "Filter-enhanced adiabatic quantum computing on a digital quantum processor", Physical Review Research 7 3, 033153 (2025).

[3] Thilo R. Müller, Manuel Geiger, and Christian B. Mendl, "Ground-State Preparation of the Fermi-Hubbard Model on a Quantum Computer with 2D Topology via Quantum Eigenvalue Transformation of Unitary Matrices", arXiv:2411.18535, (2024).

[4] Ruhee D'Cunha, Cristian L. Cortes, Laura Gagliardi, and Stephen K. Gray, "Fragment-based initialization for quantum subspace methods", Physical Review A 110 4, 042613 (2024).

[5] Zikang Jia, Suying Liu, and Yulong Dong, "Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing", arXiv:2604.01205, (2026).

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