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A quantum computer is computing device that makes use of quantum state instead of classical states. A quantum state, also known as a state vector, contains statistical information about the quantum system. It’s essentially a probability density. Quantum states can have interesting properties like superposition, entanglement, and interference effects. Now, a ...


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Superposition applies to quantum computing with the basic example of the Hadamard (H) gate which creates a superposition on the target qubit. The H gate is essential in constructing quantum algorithms such as Shor's Algorithm and Grover's Algorithm (for example).


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Note that the two bases in the Schmidt decomposition do not necessarily coincide (for reasons related to the fact that the two unitary matrices in the singular value decomposition do not necessarily coincide). It is therefore clearer to write $$ |\psi \rangle = \lambda_0 |\phi_0^A \rangle |\phi_0^B \rangle + \lambda_1 |\phi_1^A \rangle |\phi_1^B \rangle $$ ...


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how one evaluation of $U_f$ on $\left|+^n\right>$ only requires one query of our black box $f$ It doesn't. There are two black boxes. The quantum black box $U_f$ is the quantum counterpart of the classical black box $f$. In analyzing the query complexity of the classical search algorithm we count the number of times the algorithm invokes the classical ...


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