Gunjan, Gunjan and G, Ramesh
(2015)
Quantum Computing.
Masters thesis, Indian Institute of Technology Hyderabad.
Abstract
Linear algebra that will be needed for the rest of thesis.
We begin by defining linear operators on vector spaces. we define physics Bra-Ket notation that
will be used throughout the thesis. The next few sections deal with topics related to matrices
like Trace,Unitary, Hermitian and Positive and Positive semi definite matrices. We define vector
spaces with some additional structures which includes inner product space, Outer product, Hilbert
space. we study how to make new spaces from the given spaces which includes direct sum of
vector spaces, Tensor product. Tensor product of spaces plays an important role in various area
of Quantum mechanics (we will study in next few chapters). we close this chapters with some
applications of Tensor product.
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