By Phillip Kaye, Raymond Laflamme, Michele Mosca

ISBN-10: 0198570007

ISBN-13: 9780198570004

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. geared toward complicated undergraduate and starting graduate scholars in those disciplines, the textual content is technically specified 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. even if, previous familiarity with issues similar to tensor items and spectral decomposition isn't required, because the valuable fabric is reviewed within the textual content.

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This implies that the laws of physics ultimately dictate the capabilities of any information-processing machine. So it is only reasonable to consider the laws of physics when we study the theory of information processing and in particular the theory of computation. Up until the turn of the twentieth century, the laws of physics were thought to be what we now call classical. Newton’s equations of motion and Maxwell’s equations of electromagnetism predicted experimentally observed phenomena with remarkable accuracy and precision.

TEAM LinG 40 QUBITS AND THE FRAMEWORK OF QUANTUM MECHANICS decomposed unique as a product eiθ |α| where |α| is the non-negative real number α has norm 1. The value θ is corresponding to the magnitude of α, and eiθ = |α| iθ known as the ‘phase’, and we refer to the value e as a ‘phase factor’. The condition that the state is described by a unit vector means that |α0 |2 + |α1 |2 = 1. This condition is sometimes called the normalization constraint, and it is necessary for consistency with the way quantum measurements behave, as we will see in the Measurement Postulate.

1) The outer product of a vector |ψ with itself is written |ψ ψ| and deﬁnes a linear operator that maps |ψ ψ||ϕ → |ψ ψ|ϕ = ψ|ϕ |ψ . 2) That is, the operator |ψ ψ| projects a vector |ϕ in H to the 1-dimensional subspace of H spanned by |ψ . 7). 4. 2 Let B = {|bn } be an orthonormal basis for a vector space H. 3) bn ,bm ∈B where Tn,m = bn |T |bm . 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).

### An Introduction to Quantum Computing by Phillip Kaye, Raymond Laflamme, Michele Mosca

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