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from qutip import *
RealNumber = float; Integer = int

q = Qobj([[1], [0]])
q
Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket Qobj data = [[ 1.] [ 0.]] 
# the dimension, or composite Hilbert state space structure
q.dims
[[2], [1]] 
# the shape of the matrix data representation
q.shape
[2, 1] 
# the matrix data itself. in sparse matrix format.
q.data
<2x1 sparse matrix of type '<type 'numpy.complex128'>' with 1 stored elements in Compressed Sparse Row format> 
# get the dense matrix representation
q.full()
array([[ 1.+0.j], [ 0.+0.j]]) 
# some additional properties
q.isherm, q.type
(False, 'ket') 
sy = Qobj([[0,-1j], [1j,0]])  # the sigma-y Pauli operator

sy
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True Qobj data = [[ 0.+0.j 0.-1.j] [ 0.+1.j 0.+0.j]] 
sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator

sz
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True Qobj data = [[ 1. 0.] [ 0. -1.]] 
# some arithmetic with quantum objects

H = 1.0 * sz + 0.1 * sy

print("Qubit Hamiltonian = \n")
H
Qubit Hamiltonian = Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True Qobj data = [[ 1.+0.j 0.-0.1j] [ 0.+0.1j -1.+0.j ]] 
# The hermitian conjugate
sy.dag()
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True Qobj data = [[ 0.+0.j 0.-1.j] [ 0.+1.j 0.+0.j]] 
# The trace
H.tr()
0.0 
# Eigen energies
H.eigenenergies()
array([-1.00498756, 1.00498756])