![]() ![]() sqrtm () Out: Quantum object: dims =, ], shape =, type = oper, isherm = True Qobj data = ] In : coherent_dm ( 5, 1 ). diag () Out: array() In : coherent_dm ( 5, 1 ). dag () Out: Quantum object: dims =, ], shape =, type = bra Qobj data = ] In : coherent_dm ( 5, 1 ) Out: Quantum object: dims =, ], shape =, type = oper, isherm = True Qobj data = ] In : coherent_dm ( 5, 1 ). In : basis ( 5, 3 ) Out: Quantum object: dims =, ], shape =, type = ket Qobj data = ] In : basis ( 5, 3 ). Like attributes, the quantum object class has defined functions (methods) that operate on Qobj class instances. In : basis ( 5, 3 ) Out: Quantum object: dims =, ], shape =, type = ket Qobj data = ] In : coherent ( 5, 0.5 - 0.5j ) Out: Quantum object: dims =, ], shape =, type = ket Qobj data = ] In : destroy ( 4 ) Out: Quantum object: dims =, ], shape =, type = oper, isherm = False Qobj data = ] In : sigmaz () Out: Quantum object: dims =, ], shape =, type = oper, isherm = True Qobj data = ] In : jmat ( 5 / 2.0, '+' ) Out: Quantum object: dims =, ], shape =, type = oper, isherm = False Qobj data = ] Therefore, QuTiP includes predefined objects for a variety of states: StatesĪs an example, we give the output for a few of these functions: Even more so when most objects correspond to commonly used types such as the ladder operators of a harmonic oscillator, the Pauli spin operators for a two-level system, or state vectors such as Fock states. Manually specifying the data for each quantum object is inefficient. Generating Random Quantum States & Operators.Visualization of quantum states and processes. ![]() Time Evolution and Quantum System Dynamics.Using Tensor Products and Partial Traces.Checking Version Information using the About Function.On Wolfram|Alpha Permutation Cite this as: ![]() Skiena,ĭiscrete Mathematics: Combinatorics and Graph Theory with Mathematica. "Permutations: Johnson's' Algorithm."įor Mathematicians. "Permutation Generation Methods." Comput. Knuth,Īrt of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed. "Generation of Permutations byĪdjacent Transpositions." Math. "Permutations by Interchanges." Computer J. "Arrangement Numbers." In Theīook of Numbers. The permutation which switches elements 1 and 2 and fixes 3 would be written as (2)(143) all describe the same permutation.Īnother notation that explicitly identifies the positions occupied by elements before and after application of a permutation on elements uses a matrix, where the first row is and the second row is the new arrangement. ![]() There is a great deal of freedom in picking the representation of a cyclicĭecomposition since (1) the cycles are disjoint and can therefore be specified inĪny order, and (2) any rotation of a given cycle specifies the same cycle (Skienaġ990, p. 20). This is denoted, corresponding to the disjoint permutation cycles (2)Īnd (143). The unordered subsets containing elements are known as the k-subsetsĪ representation of a permutation as a product of permutation cycles is unique (up to the ordering of the cycles). (Uspensky 1937, p. 18), where is a factorial. ![]()
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