Mathematics of Quantum Computation
Among the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science.
Mathematics of Quantum Computation brings together leading computer scientists, mathematicians, and physicists to provide the first interdisciplinary but mathematically focused exploration of the field's foundations and state of the art. Each section of the book addresses an area of major research, and does so with introductory material that brings newcomers quickly up to speed. Chapters that are more advanced include recent developments not yet published in the open literature.
Information technology will inevitably enter into the realm of quantum mechanics, and, more than all the atomic, molecular, optical, and nanotechnology advances, it is the device-independent mathematics that is the foundation of quantum computer and information science. Mathematics of Quantum Computation offers the first up-to-date coverage that has the technical depth and breadth needed by those interested in the challenges being confronted at the frontiers of research.
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Chapter 2 Kinematics of qubit pairs
the case of 3 qubits
Chapter 4 Universal quantum gates
Chapter 5 From coupled pendulums to quantum search
continuous time and discrete time
general unitary transformations
Chapter 8 Counting complexity and quantum computation
Chapter 9 Algorithmic aspects of quantum errorcorrecting codes
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2-qubit 2-qudit gates Alice amplitude atom AWPP Bell cavity classical Clifford codes complexity construction corresponding CSS code decomposable decomposition defined denote detected dimension eigenstates eigenvalues elements entangled equation error control codes error correction error group error operators error-correcting codes example finite follows function GapP given Grover’s Hadamard Hadamard transform Hilbert space inequality input integer invariant irreducible king’s Lemma length Lett linear matrix measurement nice error obtained optimal LSD oracle orthogonal orthonormal basis output Pauli matrices pendulum photon Phys physicist polynomial ppure problem proof Proposition QECC quantum algorithm quantum circuit quantum codes quantum computation quantum error control quantum error-correcting codes quantum mechanics quantum systems quantum teleportation qubit pairs qubits qudits rank representation result scheme Section separable Shor stabilizer codes subgroup subspace superposition Theorem theory unitary operator unitary transformations variables vector zero