{"paper":{"title":"Efficient state preparation for multivariate Monte Carlo simulation","arxiv_id":"2409.07336","primary_cat":"quant-ph","submitted_at":"2024-09-11T15:16:35+00:00","version_compiled":"v1"},"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. 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areas.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.3,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.0,"background":0.65,"limitation":0.0,"future_work":0.0,"contribution":0.34,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":false,"role":"background","text":"Specifically in finance, multivariate state preparation is required for multivariate Monte Carlo simulation, which is used for important numerical tasks such as risk aggregation and multi-asset derivative pricing.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"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":3,"p":0.53,"id":"s3","own":false,"role":"background","text":"Using existing methods, multivariate quantum state preparation requires the number of gates exponential in the number of variables $D$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.45,"method":0.0,"result":0.0,"background":0.53,"limitation":0.02,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.88,"id":"s4","own":true,"role":"contribution","text":"For this task, we propose a quantum algorithm that only requires the number of gates linear in $D$.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.92,"main_claim_p":0.81,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.12,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.88,"interpretation":0.0}},{"i":5,"p":0.9,"id":"s5","own":false,"role":"method","text":"Our algorithm utilizes multivariable quantum signal processing (M-QSP), a technique to perform the multivariate polynomial transformation of matrix elements.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.24,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.9,"result":0.0,"background":0.02,"limitation":0.0,"future_work":0.0,"contribution":0.08,"interpretation":0.0}},{"i":6,"p":0.99,"id":"s6","own":true,"role":"method","text":"Using easily prepared block-encodings corresponding to each variable, we apply the M-QSP to construct the target function.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.99,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":7,"p":0.43,"id":"s7","own":true,"role":"result","text":"In this way, our algorithm prepares the target state efficiently for functions achievable with 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