Linear combination

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Community · Quantum logic gate

Summary

In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results.

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mathematical basis for qubit superposition
The state of a qubit is defined as a linear combination of the basis states |0⟩ and |1⟩, using complex probability amplitudes.
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enabling physical principle
Superposition allows quantum systems to exist in multiple states simultaneously, which is the primary mechanism for the parallel processing capabilities of quantum computers.
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mathematical basis for quantum gate state transformation
Quantum logic gates act on qubits by transforming their state, which is represented as a linear combination of basis states, through matrix multiplication.
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