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PreprintCC BY 4.0arXiv

Quantum algorithm for PageRank computation through multistep quantum resonant transitions

  • Chuqing Wang
  • Hefeng Wang
  • Hua Xiang
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Abstract

We present a quantum algorithm for obtaining a quantum state that encodes the PageRank vector of the Google matrix through multistep quantum resonant transition (mQRT). In the algorithm, the PageRank vector is encoded in the ground state of a problem Hamiltonian associated with the Google matrix. By dividing the web graph corresponding to the Google matrix into a series of subgraphs with nested structure, we construct a sequence of Hamiltonians based on the subgraphs to form a Hamiltonian evolution path from a simple initial Hamiltonian to the problem Hamiltonian. The ground state of the problem Hamiltonian is obtained by going through ground states of the intermediate Hamiltonians via QRT step by step. This algorithm requires only one ancillary qubit, and the runtime of the algorithm is proportional to the number of steps. It provides a new way for efficiently obtaining the quantum state of the PageRank vector of large-scale networks.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026quantum,
  title = {{Quantum algorithm for PageRank computation through multistep quantum resonant transitions}},
  author = {Chuqing Wang and Hefeng Wang and Hua Xiang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08140},
  eprint = {2609.08140},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08140},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantum algorithm for PageRank computation through multistep quantum resonant transitions
AU  - Chuqing Wang
AU  - Hefeng Wang
AU  - Hua Xiang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08140
UR  - https://arxiv.org/abs/2609.08140
AB  - We present a quantum algorithm for obtaining a quantum state that encodes the PageRank vector of the Google matrix through multistep quantum resonant transition (mQRT). In the algorithm, the PageRank vector is encoded in the ground state of a problem Hamiltonian associated with the Google matrix. By dividing the web graph corresponding to the Google matrix into a series of subgraphs with nested structure, we construct a sequence of Hamiltonians based on the subgraphs to form a Hamiltonian evolution path from a simple initial Hamiltonian to the problem Hamiltonian. The ground state of the problem Hamiltonian is obtained by going through ground states of the intermediate Hamiltonians via QRT step by step. This algorithm requires only one ancillary qubit, and the runtime of the algorithm is proportional to the number of steps. It provides a new way for efficiently obtaining the quantum state of the PageRank vector of large-scale networks.
ER  -