On low-depth algorithms for quantum phase estimation

Hongkang Ni; Haoya Li; Lexing Ying

doi:10.22331/q-2023-11-06-1165

On low-depth algorithms for quantum phase estimation

Hongkang Ni¹, Haoya Li², and Lexing Ying^2,1

¹Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305
²Department of Mathematics, Stanford University, Stanford, CA 94305

Published:	2023-11-06, volume 7, page 1165
Eprint:	arXiv:2302.02454v4
Doi:	https://doi.org/10.22331/q-2023-11-06-1165
Citation:	Quantum 7, 1165 (2023).

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Abstract

Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant mismatch, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the overlap between the initial state and the target state approaches one. In this paper, we prove that an existing algorithm from quantum metrology can achieve the first three requirements. As a second contribution, we propose a modified version of the algorithm that also meets the fourth requirement, which makes it particularly attractive for early fault-tolerant quantum devices.

Featured image: The top panel illustrates the simple process of iterative improvement of estimation. The bottom panels showcase our proposed method's superior or comparable performance to the previously proposed QCELS method and its superiority over the textbook-version QPE.

► BibTeX data

@article{Ni2023lowdepthalgorithms,
  doi = {10.22331/q-2023-11-06-1165},
  url = {https://doi.org/10.22331/q-2023-11-06-1165},
  title = {On low-depth algorithms for quantum phase estimation},
  author = {Ni, Hongkang and Li, Haoya and Ying, Lexing},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1165},
  month = nov,
  year = {2023}
}

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