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Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation

Quantum Journal

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Researchers Qilin Li, Atharva Vidwans, Yazhen Wang, and Micheline B. Soley introduced Bayesian Iterative Quantum Amplitude Estimation (BIQAE), a novel method combining Bayesian statistics with quantum algorithms to enhance measurement efficiency. BIQAE outperforms existing Quantum Amplitude Estimation (QAE) approaches in both accuracy and computational efficiency, as demonstrated through rigorous mathematical proofs and numerical simulations across chemistry and finance applications. The framework provides rigorous interval estimates at every iteration, reducing uncertainty and accelerating convergence in quantum simulations, particularly for molecular ground-state energy calculations. Analytical and numerical sample complexity analyses confirm BIQAE’s superiority, achieving high precision with fewer quantum measurements than prior methods. This work highlights Bayesian statistics as a powerful tool to expedite quantum utility, suggesting broader implications for quantum-classical hybrid algorithms in near-term quantum computing.

Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation

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AbstractWe establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.► BibTeX data@article{Li2026harnessingbayesian, doi = {10.22331/q-2026-01-14-1962}, url = {https://doi.org/10.22331/q-2026-01-14-1962}, title = {Harnessing {B}ayesian {S}tatistics to {A}ccelerate {I}terative {Q}uantum {A}mplitude {E}stimation}, author = {Li, Qilin and Vidwans, Atharva and Wang, Yazhen and Soley, Micheline B.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1962}, month = jan, year = {2026} }► References [1] Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp. ``Quantum amplitude amplification and estimation''. In Samuel J Lomonaco, Jr. and Howard E Brandt, editors, Quantum Computation and Information (Washington, DC, 2000). Volume 305, pages 53–74. AMS Contemporary Mathematics (2002). https://doi.org/10.1090/conm/305/05215 [2] Lov K. Grover. ``A framework for fast quantum mechanical algorithms''. In Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing. Pages 53–62. Association for Computing Machinery (1998). https://doi.org/10.1145/276698.276712 [3] Daniel S. Abrams and Colin P. Williams. ``Fast quantum algorithms for numerical integrals and stochastic processes'' (1999). arXiv:quant-ph/9908083. https://doi.org/10.48550/arXiv.quant-ph/9908083 arXiv:quant-ph/9908083 [4] Chu-Ryang Wie. ``Simpler quantum counting''. Quantum Information and Computation 19, 967–983 (2019). https://doi.org/10.26421/QIC19.11-12-5 [5] Scott Aaronson and Patrick Rall. ``Quantum approximate counting, simplified''. In Symposium on Simplicity in Algorithms. Pages 24–32. SIAM (2020). https://doi.org/10.1137/1.9781611976014.5 [6] Kouhei Nakaji. ``Faster amplitude estimation''. Quantum Information and Computation 20, 1109–1123 (2020). https://doi.org/10.26421/QIC20.13-14-2 [7] Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto. ``Amplitude estimation without phase estimation''.

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Econometrica 50, 1–25 (1982). https://doi.org/10.2307/1912526Cited byCould not fetch Crossref cited-by data during last attempt 2026-01-14 10:56:27: Could not fetch cited-by data for 10.22331/q-2026-01-14-1962 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-01-14 10:56:27: No response from ADS or unable to decode the received json data when getting the list of citing works.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. AbstractWe establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.► BibTeX data@article{Li2026harnessingbayesian, doi = {10.22331/q-2026-01-14-1962}, url = {https://doi.org/10.22331/q-2026-01-14-1962}, title = {Harnessing {B}ayesian {S}tatistics to {A}ccelerate {I}terative {Q}uantum {A}mplitude {E}stimation}, author = {Li, Qilin and Vidwans, Atharva and Wang, Yazhen and Soley, Micheline B.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {1962}, month = jan, year = {2026} }► References [1] Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp. ``Quantum amplitude amplification and estimation''. 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SIAM (2020). https://doi.org/10.1137/1.9781611976014.5 [6] Kouhei Nakaji. ``Faster amplitude estimation''. Quantum Information and Computation 20, 1109–1123 (2020). https://doi.org/10.26421/QIC20.13-14-2 [7] Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto. ``Amplitude estimation without phase estimation''.

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Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation

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