Heisenberg-limited Bayesian phase estimation with low-depth digital quantum circuits
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1.
California Institute of Technology
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2.
Tel Aviv University
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3.
Hebrew University of Jerusalem
Abstract
Optimal phase estimation protocols require complex state preparation and readout schemes, generally unavailable or unscalable in many quantum platforms. We develop a scheme that achieves near-optimal precision up to a constant overhead for Bayesian phase estimation, using simple digital quantum circuits with depths scaling logarithmically with the number of qubits. This is done by approximating the optimal initial states with products of Greenberger-Horne-Zeilinger states for Gaussian prior phase distributions with arbitrary widths. We study various protocols that employ this class of states with different levels of measurement and post-processing complexities, and obtain improvement compared to previously proposed schemes. We then use our scheme to address phase slip errors and laser noise, which impose a major limitation in Bayesian phase estimation and atomic clocks. Based on our scheme, we develop an efficient protocol to suppress this noise that outperforms existing methods.
Copyright and License
© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Acknowledgement
We thank Elie Bataille, Yanbei Chen, Rafał Demkowicz-Dobrzański, Klemens Hammerer, and Raphael Kaubruegger for their helpful discussions. We acknowledge funding from the Army Research Office MURI program (W911NF2010136) and from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907). R.F. acknowledges support from the Troesh postdoctoral fellowship. T.G. acknowledges funding provided by the Institute for Quantum Information and Matter.
Data Availability
The data generated in this manuscript can be found at github.com/sudirekci/GHZ_Blocks.
Code Availability
The codes used to generate the results are available from the corresponding author upon reasonable request.
Supplemental Material
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Additional details
Related works
- Describes
- Journal Article: https://rdcu.be/eZU92 (ReadCube)
- Is new version of
- Discussion Paper: arXiv:2407.06006 (arXiv)
Funding
- Army Research Office MURI program
- W911NF2010136
- National Science Foundation
- PHY-1733907
- California Institute of Technology
Dates
- Submitted
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2025-06-30
- Accepted
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2025-12-25
Caltech Custom Metadata
- Caltech groups
- Institute for Quantum Information and Matter , Division of Physics, Mathematics and Astronomy (PMA)
- Publication Status
- In Press