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In a di erent direction, Nielsen [565] showed that projective measurements can be used in the place of quantum gates as the fundamental primitive for QC This was followed by the results of Raussendorf and Briegel [566] showing how to perform QC by preparing certain highly entangled cluster states, followed by a sequence of measurements Adiabatic QC, rst proposed by Farhi et al [542] and then generalized by Aharonov et al [476, 477], starts with an initial state that is the ground state of a sum of local Hamiltonians, and then gradually transforms to a di erent sum of local Hamiltonians whose ground state is closely related to the desired output of the QC Aharonov et al showed that this model is exactly as powerful as the quantum circuit model, thus providing another potential implementation of QC The nontrivial spectral gap gives this model some natural fault-tolerant properties.

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The role of entanglement in the power of QC is a fundamental theme Two questions about this issue have arisen in the context of liquid NMR QC The rst question asks about the computational power of a mixed-state quantum computer whose state is required to be separable at every time step of the computation Caves and Schack [567] pointed out that even though at rst glance this model appears to be classical (because there is no entanglement), we do not know how to simulate it classically; nor do we know how to perform nontrivial QC with it Another model, proposed by Knill and La amme [568] consists of 1 clean qubit with n 1 qubits in the maximally mixed state Pulin et al [569] give a quantum algorithm in this model to measure the average delity decay of a quantum map under perturbation..

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Equation (4.4) represents a system of straight fringes that are equally spaced and perpendicular to the x direction (direction of shear). This situation is illustrated in Figure 4.4(a). The straight fringes appear in the common area of the overlapping wavefronts. If there is no defocusing D 0 , there are no fringes. The area of wavefront overlap appears to be of uniform intensity, corresponding to the same optical path for both beams. Tilt. When the wavefront is laterally sheared, normally we assume that the new wavefront is not tilted with respect to the original wavefront. In certain arrangements, however, it is possible to obtain a known amount of tilt between the two wavefronts. In such cases, it is a usual practice to obtain the tilt in the direction orthogonal to that of the lateral shear. The optical path difference associated with this tilt may be represented as a linear function of the y coordinate. Thus, in the case of only tilt, we nd W x; y Ey nl: 4:5

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Figure 3.15 (A) A pediatric CR image, with white background (arrows) as seen on a video monitor. (B) A better visual quality image after the white background is automatically removed.

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