[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121820-en":3,"doc-seo-121820-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},121820,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Estimating truncation effects of quantum bosonic systems using sampling algorithms","Simulating bosonic theories on qubit- or qudit-based quantum computers requires regularization via truncating infinite-dimensional local Hilbert spaces to finite dimensions. The work targets the practical question of how large truncation errors can become without access to a high-end quantum computer. It demonstrates that classical sampling, especially Markov Chain Monte Carlo, can estimate truncation effects for a broad class of bosonic systems. The approach is applied to ϕ4 scalar field theory on a 2D lattice beyond exact diagonalization, enabling resource estimation and validation of quantum simulation results.","Machine Learning: Science and  \nTechnology   \nPAPER • OPEN ACCESS  \nEstimating truncation effects of quantum bosonic systems using sampling algorithms  \nTo cite this article: Masanori Hanada et al 2023 Mach. Learn. : Sci. Technol. 4 045021  \nView the article online for updates and enhancements.  \nYou may also like  \n-Mass Calibration of Optically Selected DES Clusters Using a Measurement of CMB-cluster Lensing with SPTpol Data  \nS. Raghunathan, S. Patil, E. 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Technol. 4 (2023) 045021 [https://doi.org/10.1088/2632-2153/ad035c](https://doi.org/10.1088/2632-2153/ad035c)  \nOPEN ACCESS  \nRECEIVED  \n30 March 2023  \nREVISED  \n31 August 2023  \nACCEPTED FOR PUBLICATION 13 October 2023  \nPUBLISHED  \n30 October 2023  \nOriginal Content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nPAPER  \nEstimating truncation effects of quantum bosonic systems using sampling algorithms  \nMasanori Hanada1,2, ∗, Junyu Liu2,3,4,5, 11􀁂, Enrico Rinaldi6,7,8,9 and Masaki Tezuka10􀁂  \n1 School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom  \n2 qBraid Co., Harper Court 5235, Chicago, IL 60615, United States of America  \n3 Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, United States of America  \n4 Chicago Quantum Exchange, Chicago, IL 60637, United States of America  \n5 Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL 60637, United States of America  \n6 Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan  \n7 Physics Department, University of Michigan, Ann Arbor, MI 48109, United States of America  \n8 Theoretical Quantum Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan  \n9 Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Program, RIKEN, Wako, Saitama 351-0198, Japan  \n10 Department of Physics, Kyoto University, Kyoto 606-8502, Japan  \n11 SeQure, Chicago, IL 60637, United States of America  \n∗ Author to whom any correspondence should be addressed.  \n[E-mail: m.hanada@qmul.ac.uk](E-mail: m.hanada@qmul.ac.uk)  \nKeywords: quantum simulation, bosonic theory, Hilbert space truncation, Markov Chain Monte Carlo, scalar field theory, quantum computation, error estimation  \nAbstract  \nTo simulate bosons on a qubit-or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.  \n1. Introduction  \nThe Hilbert ","cbCaihzovQZWvZLB","https://ap.wps.com/l/cbCaihzovQZWvZLB","pdf",749248,1,14,"English","en",105,"# Introduction\n## Truncation (digitization) of bosonic Hilbert spaces\n## Estimating digitization errors with classical algorithms\n## Challenges and prior work on truncated bosonic systems\n## Case study: ϕ4 scalar field theory on a 2D lattice","[{\"question\":\"Why is Hilbert space truncation needed when simulating bosons on quantum computers?\",\"answer\":\"Bosonic local Hilbert spaces are infinite-dimensional, so practical quantum simulations require truncating them to finite dimensions to implement the theory on qubit- or qudit-based hardware.\"},{\"question\":\"What classical method does the paper use to estimate truncation errors?\",\"answer\":\"The paper uses traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, to estimate how large truncation errors can be.\"},{\"question\":\"How is the method demonstrated in the paper?\",\"answer\":\"It is applied to ϕ4 scalar field theory on a two-dimensional lattice with sizes beyond those achievable by exact diagonalization, allowing both resource estimation and validity checks for quantum simulations.\"}]","Estimating truncation effects of quantum bosonic systems using sampling algorithms | 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is Hilbert space truncation needed when simulating bosons on quantum computers?","Question",{"text":75,"@type":76},"Bosonic local Hilbert spaces are infinite-dimensional, so practical quantum simulations require truncating them to finite dimensions to implement the theory on qubit- or qudit-based hardware.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What classical method does the paper use to estimate truncation errors?",{"text":80,"@type":76},"The paper uses traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, to estimate how large truncation errors can be.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the method demonstrated in the paper?",{"text":84,"@type":76},"It is applied to ϕ4 scalar field theory on a two-dimensional lattice with sizes beyond those achievable by exact diagonalization, allowing both resource estimation and validity checks for quantum 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