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Constructive quantum Shannon decomposition from Cartan involutions

Byron Drury, Peter Love
2008 Journal of Physics A: Mathematical and Theoretical  
This insight gives a simple constructive algorithm for obtaining the Quantum Shannon Decomposition of a given unitary matrix in terms of the corresponding Cartan involutions.  ...  We obtain the basis of the circuit's design in a pair of Cartan decompositions.  ...  If L is a non-zero Lie algebra and Rad L = 0, we call L semi-simple.  ... 
doi:10.1088/1751-8113/41/39/395305 fatcat:6jzz4zrzlnec5lfe6hskevzjve

Refining expression DAGs in exact-decisions number types [article]

Martin Wilhelm, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Stefan Schirra
Error bound balancing is very versatile and can reduce a large amount of the cost associated with unbalanced structures.  ...  Exact number types play a central role in the development of robust algorithms in the field of computational geometry, where combinatorial decisions are made on the basis of numerical computations.  ...  The red lines represent a separation bound. The interval [a 1 , b 1 ] contains zero and values whose size is larger than the separation bound.  ... 
doi:10.25673/32582 fatcat:nwxz6me4nfgchkf5e2rdxtmwdq

Algorithm engineering for expression dag based number types [article]

Marc Andreas Mörig, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Stefan Schirra
The framework separates five key components of such a strategy: basic arithmetic, maximum number of summands, handling floating-point exceptions, reducing the number of summands, and switching to an expression  ...  b − − 3 − 11 × 6 2 a 12 + 144 + 20 + 3 4 7 + 5 × 11 = 9 2 + 0 A dozen, a gross, and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit  ...  Zero Separation Bounds. If expressions are evaluated approximately only, separation bounds allow to identify nodes with a value of zero.  ... 
doi:10.25673/4246 fatcat:ytxch2negzf4hjlvyao2ds7om4