By Phillip Kaye, Raymond Laflamme, Michele Mosca
This concise, available textual content offers an intensive 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 distinct and is obviously illustrated all through with diagrams and workouts. a few earlier wisdom of linear algebra is thought, together with vector areas and internal items. although, past familiarity with subject matters comparable to tensor items and spectral decomposition isn't really required, because the useful fabric is reviewed within the textual content.
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Additional info for An Introduction to Quantum Computing
G. |ϕ ) to index diﬀerent terms in a superposition i of states on a single system. 3 where we used subscripts on |ψ1 and |ψ2 to index states on diﬀerent subsystems of a bipartite system (factors in a tensor product). Both conventions are commonly used, and the meaning should always be clear from the context. TEAM LinG 50 QUBITS AND THE FRAMEWORK OF QUANTUM MECHANICS |ψ = 6 11 |0 1 6 |0 3 5 |1 . 5) The measurement of just the ﬁrst qubit gives 0 with probability 6 11 , and in this + 5 6 |1 + 5 11 |1 2 5 |0 + 1 6 |0 case the state of the second qubit is left in the superposition + 5 6 |1 .
A11 Bp1 . . A11 Bpq . . . A1n Bp1 . . A1n Bpq ⎥ ⎢ ⎥ ⎢ ⎥ .. .. .. .. ⎢ ⎥ . . . . ⎥. 7) ⎢ ⎥ .. .. .. .. ⎢ ⎥ . . . . ⎢ ⎥ ⎢Am1 B11 . . Am1 B1q . . . Amn B11 . . Amn B1q ⎥ ⎢ ⎥ ⎢ ⎥ .. .. .. .. ⎣ ⎦ . . . . Am1 Bp1 . . Am1 Bpq . . . Amn Bp1 . . Amn Bpq This matrix is sometimes written more compactly in ‘block form’ as ⎤ ⎡ A11 [B] A12 [B] . . A1n [B] ⎢ A21 [B] A22 [B] . . A2n [B] ⎥ ⎥ ⎢ A⊗B =⎢ . ⎥. .. ⎦ ⎣ .. . 8) Am1 [B] Am2 [B] .
It is equal to its own Hermitean conjugate). 7 A projector on a vector space H is a linear operator P that satisﬁes P 2 = P . 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.
An Introduction to Quantum Computing by Phillip Kaye, Raymond Laflamme, Michele Mosca