Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.
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One-way quantum computer
The one-way or measurement based quantum computer is a method of quantum computing that first prepares an entangled resource state, usually a cluster state or graph state, then performs single qubit measurements on it. It is "one-way" because the resource state is destroyed by the measurements. The outcome of each individual measurement is random, but they are related in such a way that the computation always succeeds.
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Quantum computer
A quantum computer is a device for computation that makes direct use of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from digital computers based on transistors. Whereas digital computers require data to be encoded into binary digits, quantum computation utilizes quantum properties to represent data and perform operations on these data.
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Quantum entanglement
Quantum entanglement occurs when particles such as photons, electrons, molecules as large as buckyballs, and even small diamonds interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description, which is indefinite in terms of important factors such as position, momentum, spin, polarization, etc.
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Unitary operator
In functional analysis, a branch of mathematics, a unitary operator (not to be confused with a unity operator) is a bounded linear operator U : H ¿ H on a Hilbert space H satisfying where U is the adjoint of U, and I : H ¿ H is the identity operator. This property is equivalent to the following: U preserves the inner product ¿ , ¿ of the Hilbert space, i.e. , for all vectors x and y in the Hilbert space,, and U is surjective.
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Denotational semantics
In computer science, denotational semantics (initially known as mathematical semantics or Scott¿Strachey semantics) is an approach to formalizing the meanings of programming languages by constructing mathematical objects (called denotations) which describe the meanings of expressions from the languages. Other approaches to providing a formal semantics of programming languages include axiomatic semantics and operational semantics.
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Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content. Syntactically, p and q are equivalent if each can be proved from the other. Semantically, p and q are equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as, Epq, or . However, these symbols are also used for material equivalence; the proper interpretation depends on the context.
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