On Low-depth Algorithms For Quantum Phase Estimation

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}<br /> }

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Cited by

[1] Zhiyan Ding and Lin Lin, “Even Shorter Quantum Circuit for Phase Estimation on Early Fault-Tolerant Quantum Computers with Applications to Ground-State Energy Estimation”, PRX Quantum 4 2, 020331 (2023).

[2] Guoming Wang, Daniel Stilck França, Ruizhe Zhang, Shuchen Zhu, and Peter D. Johnson, “Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision”, arXiv:2209.06811, (2022).

[3] Haoya Li, Yu Tong, Hongkang Ni, Tuvia Gefen, and Lexing Ying, “Heisenberg-limited Hamiltonian learning for interacting bosons”, arXiv:2307.04690, (2023).

[4] Zhiyan Ding and Lin Lin, “Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers”, Quantum 7, 1136 (2023).

[5] Changhao Yi, Cunlu Zhou, and Jun Takahashi, “Quantum Phase Estimation by Compressed Sensing”, arXiv:2306.07008, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-11-11 01:03:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-11-11 01:03:05).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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On low-depth algorithms for quantum phase estimation

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On low-depth algorithms for quantum phase estimation

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