Corpus ID: 210714193

Grover's Algorithm and Many-Valued Quantum Logic

  title={Grover's Algorithm and Many-Valued Quantum Logic},
  author={Samuel Hunt and Maximilien Gadouleau},
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model, in which the information and transformations can be expressed in any arity, and analyse the structural and behavioural properties while preserving the semantics; namely, searching for the unique preimage to an output a function. We conclude by demonstrating… Expand
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This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to nvalued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguishExpand
A Generalization of the Deutsch-Jozsa Algorithm to Multi-Valued Quantum Logic
  • Yale Fan
  • Mathematics, Computer Science
  • 37th International Symposium on Multiple-Valued Logic (ISMVL'07)
  • 2007
This work generalizes the binary Deutsch-Jozsa algorithm to n- valued logic using the quantum Fourier transform and can find closed expressions for classes of affine functions in quantum oracles, accurate to a constant term. Expand
A fast quantum mechanical algorithm for database search
In early 1994, it was demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . Expand
Generalization of the Deutsch algorithm using two qudits
Deutsch's algorithm for two qubits (one control qubit plus one auxiliary qubit) is extended to two $d$-dimensional quantum systems or qudits for the case in which $d$ is equal to $2^n$, $n=1,2,...$ .Expand
Hybrid quantum computing with ancillas
This review provides an overview of the basic concepts of the gate model quantum computer architecture, including the different possible forms of information encodings – from base two up to continuous variables – and a more detailed description of how the main types of ancilla-mediated quantum operations provide efficient quantum gates. Expand
Quantum computation and quantum information
  • T. Paul
  • Mathematics, Computer Science
  • Mathematical Structures in Computer Science
  • 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers dealExpand
Quantum theory, the Church–Turing principle and the universal quantum computer
  • D. Deutsch
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1985
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizibleExpand
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  • P. Shor
  • Computer Science, Mathematics
  • SIAM Rev.
  • 1999
Efficient randomized algorithms are given for factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Expand
Quantum Computational Complexity
  • J. Watrous
  • Mathematics, Computer Science
  • Encyclopedia of Complexity and Systems Science
  • 2009
Property of quantum complexity classes based on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems are presented. Expand
Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
Abstract Design of a large-scale quantum computer has paramount importance for science and technologies. We investigate a scheme for realization of quantum algorithms using noncomposite quantumExpand