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Quantum hidden subgroup algorithms on free groups, (in preparation
"... Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In thi ..."
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Abstract. One of the most promising and versatile approaches to creating new quantum algorithms is based on the quantum hidden subgroup (QHS) paradigm, originally suggested by Alexei Kitaev. This class of quantum algorithms encompasses the DeutschJozsa, Simon, Shor algorithms, and many more. In this paper, our strategy for finding new quantum algorithms is to decompose Shor’s quantum factoring algorithm into its basic primitives, then to generalize these primitives, and finally to show how to reassemble them into new QHS algorithms. Taking an ”alphabetic building blocks approach, ” we use these primitives to form an ”algorithmic toolkit ” for the creation of new quantum algorithms, such as wandering Shor algorithms, continuous Shor algorithms, the quantum circle algorithm, the dual Shor algorithm, a QHS algorithm for Feynman integrals, free QHS algorithms, and more. Toward the end of this paper, we show how Grover’s algorithm is most surprisingly “almost ” a QHS algorithm, and how this result suggests the possibility of an even more complete ”algorithmic tookit ” beyond the QHS algorithms. Contents
A CONTINUOUS VARIABLE SHOR ALGORITHM
, 2004
"... Abstract. In this paper, we use the methods found in [21] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → R from the reals R to the reals R, where Φ belongs to a very ge ..."
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Cited by 2 (2 self)
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Abstract. In this paper, we use the methods found in [21] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → R from the reals R to the reals R, where Φ belongs to a very general class of functions, called the class of admissible functions. One objective in creating this continuous variable quantum algorithm was to make the structure of Shor’s factoring algorithm more mathematically transparent, and thereby give some insight into the inner workings of Shor’s original algorithm. This continuous quantum algorithm also gives some insight into the inner workings of Hallgren’s Pell’s equation algorithm. Two key questions remain unanswered. Is this quantum algorithm more efficient than its classical continuous variable counterpart? Is this quantum
A Novel Ternary More, Less and Equality Circuit Using SemiFloating Gate Devices
 Proceedings IEEE International Symposium on Circuits and Systems
, 2006
"... Abstract — This paper presents a novel Ternary More, Less and Equality (MLE) Circuit implemented with Recharged SemiFloating Gate Transistors. The circuit is a ternary application, and ternary structures may offer the fastest search in a tree structure. The circuit has two ternary inputs, and one t ..."
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Cited by 1 (1 self)
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Abstract — This paper presents a novel Ternary More, Less and Equality (MLE) Circuit implemented with Recharged SemiFloating Gate Transistors. The circuit is a ternary application, and ternary structures may offer the fastest search in a tree structure. The circuit has two ternary inputs, and one ternary output which will be a comparison of the two ternary inputs. The circuit is a useful building block for use in a search tree application. The circuit is simulated by using Cadence R○Analog Design Environment with CMOS090 GP process parameters from STMicroelectronics, a 90 nm General Purpose Bulk CMOS Process with 7 metal layers. The circuit operates at a 1 GHz clock frequency. The supply voltage is +/ 0.5 Volt. All capacitors are metal plate capacitors, based on a vertical coupling capacitance between stacked metal plates. I.
A Novel Balanced Ternary Adder Using Recharged SemiFloating Gate Devices
"... Abstract — This paper presents a novel voltage mode Balanced Ternary Adder (BTA), implemented with Recharged SemiFloating Gate Devices. By using balanced ternary notation, it possible to take advantage of carry free addition, which is exploited in designing a fast adder cell. The circuit operates a ..."
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Cited by 1 (0 self)
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Abstract — This paper presents a novel voltage mode Balanced Ternary Adder (BTA), implemented with Recharged SemiFloating Gate Devices. By using balanced ternary notation, it possible to take advantage of carry free addition, which is exploited in designing a fast adder cell. The circuit operates at 1 GHz clock frequency. The supply voltage is only 1.0 Volt. The circuit is simulated by using Cadence R○Analog Design Environment, with CMOS090 process parameters, a 90nm General Purpose Bulk CMOS Process from STMicroelectronics with 7 metal layers. All the capacitors are metal plate capacitors, based on vertical coupling capacitance between stacked metal plates. I.
ASPECTS OF BALANCED TERNARY ARITHMETICS IMPLEMENTED USING CMOS RECHARGED SEMIFLOATING GATE DEVICES
, 2008
"... This thesis is a part of my work for my Ph.D. in Nanoelectronic at the Microelectronics ..."
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This thesis is a part of my work for my Ph.D. in Nanoelectronic at the Microelectronics
Do All Roads Lead to Rome? (or Reductions for Dummy Travelers) †
"... Reduction is a central ingredient of computational thinking, and an important tool in algorithm design, in computability theory, and in complexity theory. Reduction has been recognized to be a difficult topic for students to learn. Previous studies on teaching reduction have concentrated on its use ..."
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Reduction is a central ingredient of computational thinking, and an important tool in algorithm design, in computability theory, and in complexity theory. Reduction has been recognized to be a difficult topic for students to learn. Previous studies on teaching reduction have concentrated on its use in special courses on the theory of computing. As a fundamental concept, reduction should be discussed multiple times during a curriculum, starting from firstyear studies. In order to support this, we propose intuitive analogies based on the metaphor of traveling that could be used as an aid for illuminating key ideas of reductions on introductory computer science courses.
Contents
, 2002
"... Abstract. In this paper, we use the methods found in [12] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → C from the reals R to the complex numbers C, where Φ belongs to ..."
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Abstract. In this paper, we use the methods found in [12] to create a continuous variable analogue of Shor’s quantum factoring algorithm. By this we mean a quantum hidden subgroup algorithm that finds the period P of a function Φ: R − → C from the reals R to the complex numbers C, where Φ belongs to a very general class of functions, called the class of admissible functions. This algorithm gives some insight into the inner workings of Shor’s quantum factoring algorithm.
SHAPE SELECTION IN SYNTHESIS OF COLLOIDS AND NANOPARTICLES
"... We address a longstanding problem in colloid and nanoparticle science: particle shape selection in solution synthesis [1]. Our main finding is that a proper balance of two processes, preferential attachment of transported ..."
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We address a longstanding problem in colloid and nanoparticle science: particle shape selection in solution synthesis [1]. Our main finding is that a proper balance of two processes, preferential attachment of transported
World J. Eng. 6, Article P909 (2009) Eprint 0903.2841 at www.arxiv.org SHAPE SELECTION IN SYNTHESIS OF COLLOIDS AND NANOPARTICLES
"... We address a longstanding problem in colloid and nanoparticle science: particle shape selection in solution synthesis [1]. Our main finding is that a proper balance of two processes, preferential attachment of transported ..."
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We address a longstanding problem in colloid and nanoparticle science: particle shape selection in solution synthesis [1]. Our main finding is that a proper balance of two processes, preferential attachment of transported