{"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/novel-oracle-constructions-for-quantum-random","title":"Novel oracle constructions for quantum random access memory","arxiv_id":"2405.20225","date":"2024-05-30","proceeding":null,"authors":["Ákos Nagy","Cindy Zhang"],"abstract":"We present new designs for quantum random access memory. More precisely, for each function, $f : \\mathbb{F}_2^n \\rightarrow \\mathbb{F}_2^d$, we construct oracles, $\\mathcal{O}_f$, with the property \\begin{equation} \\mathcal{O}_f \\left| x \\right\\rangle_n \\left| 0 \\right\\rangle_d = \\left| x \\right\\rangle_n \\left| f(x) \\right\\rangle_d. \\end{equation} Our methods are based on the Walsh-Hadamard Transform of $f$, viewed as an integer valued function. In general, the complexity of our method scales with the sparsity of the Walsh-Hadamard Transform and not the sparsity of $f$, yielding more favorable constructions in cases such as binary optimization problems and function with low-degree Walsh-Hadamard Transforms. Furthermore, our design comes with a tuneable amount of ancillas that can trade depth for size. In the ancilla-free design, these oracles can be $\\epsilon$-approximated so that the Clifford + $T$ depth is $O \\left( \\left( n + \\log_2 \\left( \\tfrac{d}{\\epsilon} \\right) \\right) \\mathcal{W}_f \\right)$, where $\\mathcal{W}_f$ is the number of nonzero components in the Walsh-Hadamard Transform. The depth of the shallowest version is $O \\left( n + \\log_2 \\left( \\tfrac{d}{\\epsilon} \\right) \\right)$, using $n + d \\mathcal{W}_f$ qubit. The connectivity of these circuits is also only logarithmic in $\\mathcal{W}_f$. As an application, we show that for boolean functions with low approximate degrees (as in the case of read-once formulas) the complexities of the corresponding QRAM oracles scale only as $2^{\\widetilde{O} \\left( \\sqrt{n} \\log_2 \\left( n \\right) \\right)}$.","url_abs":"https://arxiv.org/abs/2405.20225v2","url_pdf":"https://arxiv.org/pdf/2405.20225v2.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":"novel-oracle-constructions-for-quantum-random","repo_url":"https://github.com/akos-nagy/walshhadamardqram","is_official":1,"mentioned_in_paper":1,"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}