Quantum Fourier transform and Quantum computing

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Difference between Quantum Fourier transform and Quantum computing

Quantum Fourier transform vs. Quantum computing

In quantum computing, the quantum Fourier transform (for short: QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.

BQP

In computational complexity theory, BQP (bounded-error quantum polynomial time) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances.

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Discrete logarithm

In the mathematics of the real numbers, the logarithm logb a is a number x such that, for given numbers a and b. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that.

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Hidden subgroup problem

The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science.

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John Preskill

John Phillip Preskill (born January 19, 1953) is an American theoretical physicist and the Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech).

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Michael Nielsen

Michael Aaron Nielsen (born January 4, 1974) is a quantum physicist, science writer, and computer programming researcher living in San Francisco.

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Quantum algorithm

In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation.

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Quantum circuit

In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register.

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Quantum logic gate

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of qubits.

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Qubit

In quantum computing, a qubit or quantum bit (sometimes qbit) is a unit of quantum information—the quantum analogue of the classical binary bit.

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Shor's algorithm

Shor's algorithm, named after mathematician Peter Shor, is a quantum algorithm (an algorithm that runs on a quantum computer) for integer factorization formulated in 1994.

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Unitary matrix

In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.

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