Fundamentals of Quantum Information: Quantum Computation, by Dieter Heiss

By Dieter Heiss

Quantum details technological know-how is a swiftly constructing box that not just can provide a revolution in laptop sciences but in addition touches deeply the very foundations of quantum physics. This ebook comprises a collection of lectures by means of top specialists within the box that bridges the space among typical textbook fabric and the examine literature, therefore offering the ne- cessary heritage for postgraduate scholars and non-specialist researchers wishing to familiarize themselves with the topic completely and at a excessive point. This quantity is preferrred as a direction ebook for postgraduate scholars, and academics will locate in it a wide variety of fabric for bringing their classes up-to-date.

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Additional info for Fundamentals of Quantum Information: Quantum Computation, Communication, Decoherence and All That

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Suppose now that the original potential has two nearly degenerate minima; then in the presence of the coupling these minima remain, but are shifted away from the q-axis in opposite directions. 5)) the coupling tends to suppress the tunneling10 . It then makes eminent sense to do what one would do in the uncoupled case, namely to truncate the variable q to the two discrete values, say ±q0 /2, corresponding to the two minima and to label these in the 2-state notation by the eigenvalues ±1 of σ ˆz .

In that reference it is shown, inter alia, that the value of α = 1 is the discriminant (at zero temperature and in the limit ∆ ωc ) between two qualitatively different types of behavior of σz (t), corresponding respectively to localization (as in the case s < 1) and to Qubits, Cbits, Decoherence, Quantum Measurement and Environment 37 damped (in fact possibly overdamped) oscillation. e. σz (t) ∼ exp −Γ t, with a rate Γ which is proportional to T 2α−1 and thus is an increasing function of temperature for α > 12 but a decreasing one for α < 12 .

6) to its value for q = ± q0 . 1), with Cα given by q0 C˜α , the sum over α taken only over the low-energy (ωα < ωc ) oscillators and the effective tunneling matrix element ∆ a function of ωc . ) For a (relatively) rigorous formulation of the above argument, and a precise prescription for computing the quantity ∆(ωc ), see Section 2 and Appendix A of ref. [8]. 13) c − ω) ˜ where J(ω) may be obtained, as described above, from experiments conducted in the classical regime. e. of the “spin” components σi ) can be obtained by a variety of techniques, since the oscillators can be formally integrated out of the problem; a particularly convenient technique is the two-state functional integral method used in ref.

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