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The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group. [ABSTRACT FROM AUTHOR]

By exposing floating gates of EEPROM memory cells with frontside sample preparation, scanning nonlinear dielectric microscopy (SNDM) succeeded in reading back the data stored in the memory cells with a 250 nm node size. At an optimized voltage bias of AC = 3 V and DC = 1 V, a clear signal contrast between programmed and erased cells is obtained. The high resolution SNDM signal reveals the details of bowling-pin shape structure of memory cells, providing high confidence in data assignment during forensic applications. Such high resolution also makes SNDM a promising technique for newer generation devices with smaller node size. [ABSTRACT FROM AUTHOR]