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Geometry of abstraction in quantum computation
"... Quantum algorithms are sequences of abstract operations, performed on nonexistent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction i ..."
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Cited by 10 (7 self)
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Quantum algorithms are sequences of abstract operations, performed on nonexistent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some quantum algorithms provide feasible solutions of important hard problems, such as factoring and discrete log (which are the building blocks of modern cryptography). It is of a great practical interest to precisely characterize the computational resources needed to execute such quantum algorithms. There are many ideas how to build a quantum computer. Can we prove some necessary conditions? Categorical semantics help with such questions. We show how to implement an important family of quantum algorithms using just abelian groups and relations.
Continuous Quantum Hidden Subgroup Algorithms
, 2003
"... In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals R mod 1, i.e., the circle, and the additive group Pat ..."
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Cited by 4 (1 self)
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In this paper we show how to construct two continuous variable and one continuous functional quantum hidden subgroup (QHS) algorithms. These are respectively quantum algorithms on the additive group of reals R, the additive group R/Z of the reals R mod 1, i.e., the circle, and the additive group Paths of L 2 paths x: [0, 1] → R n in real nspace R n. Also included is a curious discrete QHS algorithm which is dual to Shor’s algorithm. Contents 1
Is Grover’s Algorithm a Quantum Hidden Subgroup Algorithm
 Journal of Quantum Information Processing
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The amplified quantum Fourier transform: solving the local period problem
 Quantum Inf Process (2013
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unknown title
, 2008
"... Algebraically connecting the hardware/software boundary using a uniform approach to highperformance computation for software and hardware applications ..."
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Algebraically connecting the hardware/software boundary using a uniform approach to highperformance computation for software and hardware applications
ABSTRACT SIMULATING QUANTUM COMPUTING: QUANTUM EXPRESS
"... Quantum Computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive na ..."
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Quantum Computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive nature of current QC hardware leaves practical testing limited to trivial examples. Thus, a robust simulator is needed to study complex QC issues. Most QC simulators model ideal operations, and thus cannot predict the actual time required to execute an algorithm or quantify the effects of errors in the calculation. We have developed a novel QC simulator that models physical hardware implementations. This simulator not only allows the accurate simulation of quantum algorithms on various hardware implementations, but also takes an important step towards providing a framework to determine their true performance and vulnerability to errors. 1
A Survey and Review of the Current StateoftheArt in Quantum Computer Programming
, 2007
"... Quantum computer programming is a new discipline emerging from interdisciplinary research in quantum computing (and several related subdisciplines including quantum information theory, mathematical physics, and measurement theory), computer science, mathematics (especially quantum logic and linear l ..."
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Quantum computer programming is a new discipline emerging from interdisciplinary research in quantum computing (and several related subdisciplines including quantum information theory, mathematical physics, and measurement theory), computer science, mathematics (especially quantum logic and linear logic), and engineering attempts to
AMPLIFIED QUANTUM TRANSFORMS
, 2014
"... In this thesis we investigate two new Amplified Quantum Transforms. In particular we create and analyze the Amplified Quantum Fourier Transform (AmplifiedQFT) and the AmplifiedHaar Wavelet Transform. The AmplifiedQFT algorithm is used to solve the following problem: The Local Period Problem: Let ..."
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In this thesis we investigate two new Amplified Quantum Transforms. In particular we create and analyze the Amplified Quantum Fourier Transform (AmplifiedQFT) and the AmplifiedHaar Wavelet Transform. The AmplifiedQFT algorithm is used to solve the following problem: The Local Period Problem: Let L = {0, 1,..., N − 1} be a set of N labels and let A be a subset of M labels of period P, i.e. a subset of the form A = {j: j = s+ rP, r = 0, 1,...,M − 1} where P ≤ √N and M << N, and where M is assumed known. Given an oracle f: L → {0, 1} which is 1 on A and 0 elsewhere, find the local period P and the offset s. First, we provide a brief history of quantum mechanics and quantum computing. Second, we examine the AmplifiedQFT in detail and compare it against the Quantum Fourier Transform (QFT) and Quantum Hidden Subgroup (QHS) algorithms for solving the Local Period Problem. We calculate the probabilities of success of each algorithm and show the AmplifiedQFT is quadratically faster than the QFT and QHS algorithms. Third, we examine the AmplifiedQFT algorithm for solving The Local Period Problem with an Error Stream. Fourth, we produce an uncertainty relation for the AmplifiedQFT algorithm. Fifth, we show how the AmplifiedHaar Wavelet Transform can solve the Local Constant or Balanced Signal Decision Problem which is a generalization of the DeutschJozsa algorithm.
unknown title
"... Abstract — Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to build the first nontrivial quantum computer. This ..."
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Abstract — Quantum computer programming is emerging as a new subject domain from multidisciplinary research in quantum computing, computer science, mathematics (especially quantum logic, lambda calculi, and linear logic), and engineering attempts to build the first nontrivial quantum computer. This paper briefly surveys the history, methods, and proposed tools for programming quantum computers circa late 2007. It is intended to provide an extensive but nonexhaustive look at work leading up to the current stateoftheart in quantum computer programming. Further, it is an attempt to analyze the needed programming tools for quantum programmers, to use this analysis to predict the direction in which the field is moving, and to make recommendations for further development of quantum programming language tools. Index Terms — quantum computing, functional programming, imperative programming, linear logic, lambda calculus I.