By Phillip Kaye, Raymond Laflamme, Michele Mosca

This concise, available textual content offers a radical advent to quantum computing - a thrilling emergent box on the interface of the pc, engineering, mathematical and actual sciences. aimed toward complex undergraduate and starting graduate scholars in those disciplines, the textual content is technically certain and is obviously illustrated all through with diagrams and routines. a few earlier wisdom of linear algebra is thought, together with vector areas and internal items. in spite of the fact that, previous familiarity with subject matters reminiscent of tensor items and spectral decomposition isn't really required, because the priceless fabric is reviewed within the textual content.

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**Extra resources for An Introduction to Quantum Computing**

**Sample text**

An orthogonal projector is a projector that also satisﬁes P† = P. Recall the following deﬁnition from basic linear algebra. 13) for some constant c. The constant c is called the eigenvalue of T corresponding to the eigenvector |ψ . The following result is relevant to measurements in quantum mechanics. 9 If T = T † and if T |ψ = λ|ψ then λ ∈ R. In other words, the eigenvalues of a Hermitean operator are real. In linear algebra one learns that the trace of a square matrix is obtained by adding the elements on the main diagonal.

13) SOME COMMENTS ON THE DIRAC NOTATION 37 In all the above examples, the bipartite space was one in which each subspace had dimension 2. The Schmidt decomposition theorem can be applied to more complicated bipartite vector space, even in cases where the two subspaces have diﬀerent dimensions. 2. 8 Some Comments on the Dirac Notation Juggling bras and kets can be somewhat confusing if you are not familiar with working in the Dirac notation. Now we discuss a convention that potentially adds to this confusion.

7) Technically we could describe quantum states by equivalence classes of unit vectors, but we will simply specify a unit vector, with the understanding that any two vectors that are related by a global phase are equivalent. We will motivate the fact that |ψ and eiθ |ψ are equivalent after we have introduced the Measurement Postulate. 3, which will be discussed shortly). Consider the analogous situation for a deterministic classical bit. The state of a classical bit can be described by a single binary value ψ, which can be equal to either 0 or 1.