By Phillip Kaye, Raymond Laflamme, Michele Mosca

This concise, available textual content presents an intensive creation to quantum computing - an exhilarating emergent box on the interface of the pc, engineering, mathematical and actual sciences. geared toward complicated undergraduate and starting graduate scholars in those disciplines, the textual content is technically special and is obviously illustrated all through with diagrams and workouts. a few earlier wisdom of linear algebra is believed, together with vector areas and internal items. although, past familiarity with subject matters akin to tensor items and spectral decomposition isn't really required, because the important fabric is reviewed within the textual content.

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

**Sample text**

Traditionally, the classical description or label is often described as a needle pointing to some value on a dial. But if we assume only ﬁnite resolution we can just as well assume a digital display with suﬃciently many digits. Quantum mechanics tells us that if the state i αi |i is provided as input to this apparatus, it will output label i with probability |αi |2 and leave the system in state |i . This is the essence of the Measurement Postulate. However, we will state a slightly more general version that can be derived from the above simple version together with the Evolution Postulate.

We know that the set of all linear operators on a vector space H forms a new complex vector space L(H) (‘vectors’ in L(H) are the linear operators on H). 2 essentially constructs a basis for L(H) out of the given basis for H. The basis vectors for L(H) are all the possible outer products of pairs of basis vectors from B, that is {|bn bm |}. TEAM LinG 28 LINEAR ALGEBRA AND THE DIRAC NOTATION The action of T is then T : |ψ → Tn,m |bn bm |ψ = bn ,bm ∈B Tn,m bm |ψ |bn . 4) bn ,bm ∈B In terms of the matrix representation of T , Tn,m is the matrix entry in the nth row and mth column.

Quantum mechanics tells us that if the state i αi |i is provided as input to this apparatus, it will output label i with probability |αi |2 and leave the system in state |i . This is the essence of the Measurement Postulate. However, we will state a slightly more general version that can be derived from the above simple version together with the Evolution Postulate. Then we will discuss other common formulations of the measurement postulate and some of their well-known features. 1) i outputs a label i with probability |αi |2 and leaves the system in state |ϕi .