[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83034-en":3,"doc-seo-83034-105":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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83034,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Hybrid Quantum Floating-Point Method for Sharp Arithmetic","Quantum algorithms require efficient encoding of random variables into quantum states, with basis encoding enabling parallel processing and straightforward representation of unsigned integers, signed integers, and fixed-/floating-point numbers. Fractional quantum representations face a trade-off between arithmetic accuracy and the circuit depth needed for manipulation. This work introduces a hybrid quantum-classical floating-point representation that stores values in a quantum register and global range/tolerance data in a classical side register. Defined addition and multiplication avoid overflow and reduce cumulative rounding-induced precision loss, achieving up to about 90% improvement in approximation after repeated additions, with applications to low-depth, high-accuracy arithmetic circuits for practical quantum computation.","arXiv :2607 .06040v1 [ quant-ph] 7 Jul 2026  \nHybrid quantum floating-point method for sharp arithmetic  \nGabriele Agliardi∗ , 1 ,2 and Enrico Prati†,3 ,4  \n∗ [gabriele.agliardi@it.ibm.com](gabriele.agliardi@it.ibm.com) † [enrico.prati@unimi.it](enrico.prati@unimi.it)  \n1 IBM Quantum, IBM Research, Via Paolo Nanni Costa 30, I–40133 Bologna, Italy  \n2 At the time of paper conception, also at Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci I–20133 Milano, Italy  \n3 Dipartimento di Fisica “Aldo Pontremoli”, Universit`a degli Studi di Milano, Via Celoria 16, I–20133 Milano, Italy  \n4 Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, I–20133 Milano, Italy  \nAbstract  \nThere are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around 90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.  \nKeywords: quantum arithmetic, quantum floating-point registers  \n1 Introduction  \nThe precision of a floating point variable degrades significantly as a result of repeated arithmetic manipulations, when the register size is fixed and a no-overflow requirement is guaranteed on all data points. Here we investigate error propagation on quantum floating point numbers when applying summation and multiplication. We propose a representation for fractional numbers, which can reduce such errors by keeping track of global properties through classical registers. The relevance of floating-point quantum arithmetic is fundamental in many application fields. Indeed, by mimicking classical arithmetic [1, 2], quantum floating-point calculations can evaluate virtually any function [3], thus allowing quantum computers to tackle data transformations of arbitrary complexity, as long as the depth and width of the circuit are supported by the hardware. In finance, for example, quantum floating point numbers are needed to represent complex payoffs in option pricing [4], as opposed to single-time and piecewise linear payoffs that can be approximated by native quantum amplitude operations [5, 6] .  \nPreviously, we studied the efficient loading of multivariate distributions by quantum generative adversarial networks [7, 8] . There, the technique finds application in the data preparation that occurs prior to the data manipulation discussed in the present manuscript. Next, we have isolated the data encoding process as a separate abstraction layer, to improve the design of quantum circuits [9] . In turn, data processing enabled by hybrid quantum floating-point arithmetic can be used to compute functions for quantum integrati","cbCaiscUQBD2b3OZ","https://ap.wps.com/l/cbCaiscUQBD2b3OZ","pdf",792403,4,1,37,"English","en",105,"# Abstract\n# Introduction\n## Precision degradation in quantum floating point\n## Related work and prior representations\n## Monoquantum coding and classical enrichment\n## Proposed hybrid side-register approach","[{\"question\":\"What problem does the hybrid quantum floating-point method address?\",\"answer\":\"It addresses precision degradation caused by repeated summation and multiplication on quantum floating-point numbers when register size is fixed and overflow must be avoided.\"},{\"question\":\"How does the proposed representation combine quantum and classical information?\",\"answer\":\"It uses a quantum register to store the floating-point values while a classical register stores global information such as range and approximation tolerances.\"},{\"question\":\"What benefit does the method provide when performing repeated arithmetic operations?\",\"answer\":\"By using the stored classical tolerance information, it significantly reduces precision loss from rounding after repeated manipulations, with examples showing up to about 90% reduction in approximation error after repeated additions.\"}]",1784184780,93,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"hybrid-quantum-floating-point-method-for-sharp-arithmetic","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/hybrid-quantum-floating-point-method-for-sharp-arithmetic/83034/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the hybrid quantum floating-point method address?","Question",{"text":75,"@type":76},"It addresses precision degradation caused by repeated summation and multiplication on quantum floating-point numbers when register size is fixed and overflow must be avoided.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed representation combine quantum and classical information?",{"text":80,"@type":76},"It uses a quantum register to store the floating-point values while a classical register stores global information such as range and approximation tolerances.",{"name":82,"@type":73,"acceptedAnswer":83},"What benefit does the method provide when performing repeated arithmetic operations?",{"text":84,"@type":76},"By using the stored classical tolerance information, it significantly reduces precision loss from rounding after repeated manipulations, with examples showing up to about 90% reduction in approximation error after repeated 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