An Introduction to Quantum Computing
Oxford University Press, Jan 18, 2007 - Mathematics - 274 pages
This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.
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LINEAR ALGEBRA AND THE DIRAC NOTATION
QUBITS AND THE FRAMEWORK OF QUANTUM
A QUANTUM MODEL OF COMPUTATION
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1-qubit gates amplitude ancilla apply bit flip black-box Bloch sphere Church-Turing Thesis classical algorithm classical computer CNOT gate codeword computational basis consider control qubit corresponding defined denote density operator described Dirac notation discrete logarithm efficiently eigenstate eigenvalue eigenvalue estimation eigenvectors encoding Equation equivalent error correction error model error operators example Exercise factor fault-tolerant finite function Hadamard gate hidden subgroup Hilbert space illustrated in Figure implement input integer linear lower bound maps Neumann measurement Note order-finding orthogonal output parity phase flip photon polynomial probabilistic Turing machine probability at least quantum algorithm quantum circuit quantum computing quantum mechanics quantum searching qubit query complexity real numbers recovery operation reversible second register Section shown in Figure simulate solution solve string subspace superposition Suppose tensor product Theorem three-bit code three-qubit Toffoli gate transformation uniformly at random unitary operator vector space wires