Ground state energy estimation and preparation by the truncated power method

Abstract

The Guided Local Hamiltonian Problem (GLHP) is the problem of ground state energy estimation and preparation given a guiding state having good overlap with the true ground state. The problem is known to be BQP-complete for small error but is classically tractable for larger error. In this work, we identify an orthogonal regime in which the problem is classically tractable, namely when the true ground state ψ has polynomially bounded ℓ₁-norm. In particular, we show that the Truncated Power Method (TPM), a classical algorithm introduced by Kirby et al. in the quantum context, has a runtime that is polynomially comparable to quantum algorithms for GLHP in all relevant parameters, except for an extra factor of |ψ|₁². In other words, if |ψ|₁² is polynomially bounded, then TPM dequantizes quantum algorithms for GLHP.

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BibTeX

@misc{chandra2026ground,
  title = {{Ground state energy estimation and preparation by the truncated power method}},
  author = {Savero Lukianto Chandra and Daochen Wang and Carolyn Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05627},
  eprint = {2610.05627},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05627},
}

RIS

TY  - UNPB
TI  - Ground state energy estimation and preparation by the truncated power method
AU  - Savero Lukianto Chandra
AU  - Daochen Wang
AU  - Carolyn Zhang
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05627
UR  - https://arxiv.org/abs/2610.05627
AB  - The Guided Local Hamiltonian Problem (GLHP) is the problem of ground state energy estimation and preparation given a guiding state having good overlap with the true ground state. The problem is known to be BQP-complete for small error but is classically tractable for larger error. In this work, we identify an orthogonal regime in which the problem is classically tractable, namely when the true ground state ψ has polynomially bounded ℓ_1-norm. In particular, we show that the Truncated Power Method (TPM), a classical algorithm introduced by Kirby et al. in the quantum context, has a runtime that is polynomially comparable to quantum algorithms for GLHP in all relevant parameters, except for an extra factor of |ψ|_1^2. In other words, if |ψ|_1^2 is polynomially bounded, then TPM dequantizes quantum algorithms for GLHP.
ER  -

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