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Elementary Quantum Gate Realizations for Multiple-Control Toffoli Gates 多控制Toffoli门的基本量子门实现
2011 41st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2011-05-23 DOI: 10.1109/ISMVL.2011.54
D. Michael Miller, R. Wille, Zahra Sasanian
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引用次数: 147
Quantum Phase Estimation Using Multivalued Logic 基于多值逻辑的量子相位估计
2011 41st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2011-05-23 DOI: 10.1109/ISMVL.2011.47
V. Parasa, M. Perkowski
{"title":"Quantum Phase Estimation Using Multivalued Logic","authors":"V. Parasa, M. Perkowski","doi":"10.1109/ISMVL.2011.47","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.47","url":null,"abstract":"Quantum phase estimation (QPE) is one of the most important quantum algorithms which is used as a subroutine for other important quantum algorithms like Shor's factoring algorithm, simulation of quantum systems, quantum counting and QFT on arbitrary Zp. In this paper we develop the theoretical framework for the multivalued quantum logic version of the QPE algorithm using d valued qudits and show a quantum circuit to implement QPE with a complexity of O(nlogn) single qudit operations. The multivalued QPE algorithm, when compared to the binary quantum logic version, turns out to be more robust and leads to a significant decrease in the number of qudits required along with drastic improvement in the precision and success probability. We derive the requirements to amplify the probability of success to a value very close to 1 (for a given precision), thereby generalizing the previously obtained result in the binary case. Also, we note that the failure probability of QPE algorithm decreases exponentially as d increases.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125984829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
A Survey on the Arity Gap 关于贫富差距的调查
2011 41st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2011-05-01 DOI: 10.1109/ISMVL.2011.20
Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser
{"title":"A Survey on the Arity Gap","authors":"Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser","doi":"10.1109/ISMVL.2011.20","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.20","url":null,"abstract":"The arity gap of a function of several variables is defined as the minimum decrease in the number of essential variables when essential variables of the function are identified. We present a brief survey on the research done on the arity gap, from the first studies of this notion up to recent developments.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128900629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
On Equational Definability of Function Classes 关于函数类的等式可定义性
2011 41st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2011-05-01 DOI: 10.1109/ISMVL.2011.19
Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser
{"title":"On Equational Definability of Function Classes","authors":"Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser","doi":"10.1109/ISMVL.2011.19","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.19","url":null,"abstract":"We propose a notion of functional equation for functions of a fixed arity, which is based on a pair of clones. We present necessary conditions for a class of functions to be definable by such equations, and show that for certain choices of clones these conditions are also sufficient.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133152787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On Composition-Closed Classes of Boolean Functions 布尔函数的复合闭类
2011 41st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2011-02-21 DOI: 10.1109/ISMVL.2011.35
Tamás Waldhauser
{"title":"On Composition-Closed Classes of Boolean Functions","authors":"Tamás Waldhauser","doi":"10.1109/ISMVL.2011.35","DOIUrl":"https://doi.org/10.1109/ISMVL.2011.35","url":null,"abstract":"We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification (diagonalization) of variables and under introduction of inessential variables (cylindrification), but they do not necessarily contain projections. Thus the lattice formed by these classes is an extension of the Post lattice. The cardinality of this lattice is continuum, yet it is possible to describe its structure to some extent.","PeriodicalId":234611,"journal":{"name":"2011 41st IEEE International Symposium on Multiple-Valued Logic","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114624452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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