{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/non-boolean-quantum-amplitude-amplification","title":"Non-Boolean Quantum Amplitude Amplification and Quantum Mean Estimation","arxiv_id":"2102.04975","date":"2021-02-09","proceeding":null,"authors":["Prasanth Shyamsundar"],"abstract":"This paper generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with non-boolean oracles. The action of a non-boolean oracle $U_\\varphi$ on an eigenstate $|x\\rangle$ is to apply a state-dependent phase-shift $\\varphi(x)$. Unlike boolean oracles, the eigenvalues $\\exp(i\\varphi(x))$ of a non-boolean oracle are not restricted to be $\\pm 1$. Two new oracular algorithms based on such non-boolean oracles are introduced. The first is the non-boolean amplitude amplification algorithm, which preferentially amplifies the amplitudes of the eigenstates based on the value of $\\varphi(x)$. Starting from a given initial superposition state $|\\psi_0\\rangle$, the basis states with lower values of $\\cos(\\varphi)$ are amplified at the expense of the basis states with higher values of $\\cos(\\varphi)$. The second algorithm is the quantum mean estimation algorithm, which uses quantum phase estimation to estimate the expectation $\\langle\\psi_0|U_\\varphi|\\psi_0\\rangle$, i.e., the expected value of $\\exp(i\\varphi(x))$ for a random $x$ sampled by making a measurement on $|\\psi_0\\rangle$. It is shown that the quantum mean estimation algorithm offers a quadratic speedup over the corresponding classical algorithm. Both algorithms are demonstrated using simulations for a toy example. Potential applications of the algorithms are briefly discussed.","url_abs":"https://arxiv.org/abs/2102.04975v1","url_pdf":"https://arxiv.org/pdf/2102.04975v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"non-boolean-quantum-amplitude-amplification","repo_url":"https://github.com/peterse/groveropt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}