{"paper":{"title":"Quantum algorithms for approximate function loading","arxiv_id":"2111.07933","primary_cat":"quant-ph","submitted_at":"2021-11-15T17:36:13+00:00","version_compiled":"v2"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.88,"id":"s1","own":false,"role":"background","text":"Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.12,"method":0.0,"result":0.0,"background":0.88,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"Here, we introduce two approximate quantum-state preparation methods for the NISQ era inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions.","hedge":{"p":0.9,"label":"asserted"},"own_p":0.91,"main_claim_p":0.24,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":3,"p":0.96,"id":"s3","own":true,"role":"result","text":"Indeed, by allowing for an infidelity $\\epsilon$ and under certain smoothness conditions, we prove that the complexity of the implementation of the Grover-Rudolph algorithm without ancillary qubits, first introduced by M\\\"ott\\\"onen $\\textit{et al}$, results into $\\mathcal{O}(2^{k_0(\\epsilon)})$, with $n$ the number of qubits and $k_0(\\epsilon)$ asymptotically independent of $n$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.68,"main_claim_p":0.32,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":4,"p":0.8,"id":"s4","own":true,"role":"interpretation","text":"This leads to a dramatic reduction in the number of required two-qubit gates.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.68,"main_claim_p":0.18,"quantitative":false,"quantitative_p":0.26,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.2,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.8}},{"i":5,"p":0.88,"id":"s5","own":true,"role":"contribution","text":"Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions.","hedge":{"p":0.94,"label":"asserted"},"own_p":0.92,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.12,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":6,"p":0.92,"id":"s6","own":true,"role":"method","text":"Our variational Ansatz is explicitly tailored to the landscape of the function, leading to a quasi-optimized number of 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