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27 relations: BQP, Discrete Fourier transform, Discrete logarithm, Eigenvalues and eigenvectors, Hadamard transform, Hermitian adjoint, Hidden subgroup problem, John Preskill, K. R. Parthasarathy (probabilist), Linear map, Matrix multiplication, Michael Nielsen, Norm (mathematics), Path integral formulation, PP (complexity), Quantum algorithm, Quantum circuit, Quantum computing, Quantum logic gate, Quantum phase estimation algorithm, Qubit, Root of unity, Shor's algorithm, Unitary matrix, Unitary operator, Unitary transformation, Vector (mathematics and physics).
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 Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
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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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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Hadamard transform
The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms.
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Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
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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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K. R. Parthasarathy (probabilist)
Kalyanapuram Rangachari Parthasarathy (born 25 June 1936) is professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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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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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory that generalizes the action principle of classical mechanics.
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PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances.
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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 computing
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
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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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Quantum phase estimation algorithm
The Quantum phase estimation algorithm (also referred to as quantum eigenvalue estimation algorithm), is a quantum algorithm to estimate the phase (or eigenvalue) of an eigenvector of a unitary operator.
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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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Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.
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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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Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.
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Unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
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Vector (mathematics and physics)
When used without any further description, vector usually refers either to.
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References
[1] https://en.wikipedia.org/wiki/Quantum_Fourier_transform
