クティップ

>>> import  qutip  
>>> import  numpy  as  np 
>>> psi  =  qutip . Qobj ([[ 0.6 ],  [ 0.8 ]])  # リストから量子状態を作成
>>> psi
量子オブジェクト: dims = [[2], [1]], shape = (2, 1), type = ket 
Qobj data = 
[[0.6] 
[0.8]] 
>>> phi = qutip . Qobj ( np . array ([ 0.8 ,  - 0.6 ]))  # numpy 配列から量子状態を作成
>>> phi
量子オブジェクト: dims = [[2], [1]], shape = (2, 1), type = ket 
Qobj data = 
[[ 0.8] 
[-0.6]] 
>>> e0 = qutip . basis ( 2 ,  0 )  # 基底ベクトルを作成
>>> e0
量子オブジェクト: dims = [[2], [1]]、shape = (2, 1)、type = ket 
Qobj data = 
[[1.] 
[0.]] 
>>> A = qutip . Qobj ( np . array ([[ 1 , 2 j ],  [ - 2 j , 1 ]]))  # numpy 配列から量子演算子を作成
>>> A
量子オブジェクト: dims = [[2], [2]]、shape = (2, 2)、type = oper、isherm = True 
Qobj data = 
[[1.+0.j 0.+2.j] 
[0.-2.j 1.+0.j]] 
>>> qutip . sigmay ()  # パウリ行列のような一般的な量子オブジェクトは、qutip パッケージで事前定義されています
。量子オブジェクト: dims = [[2], [2]]、shape = (2, 2)、type = oper、isherm = True 
Qobj data = 
[[0.+0.j 0.-1.j] 
[0.+1.j 0.+0.j]]

>>> A * qutip . sigmax () + qutip . sigmay ()  # 互換性のある形状と次元の量子オブジェクトを加算および乗算できます
量子オブジェクト: dims = [[2], [2]]、shape = (2, 2)、type = oper、isherm = False 
Qobj data = 
[[0.+2.j 1.-1.j] 
[1.+1.j 0.-2.j]] 
>>> psi . dag ()  # エルミート共役
量子オブジェクト: dims = [[1], [2]]、shape = (1, 2)、type = bra 
Qobj data = 
[[0.6 0.8]] 
>>> psi . proj ()  # 量子状態への射影
量子オブジェクト: dims = [[2], [2]]、shape = (2, 2)、type = oper、isherm = True 
Qobj data = 
[[0.36 0.48] 
[0.48 0.64]] 
>>> A . tr () # 演算子 2.0のトレース
>>> A . eigenstates () # 演算子を対角化します(array([-1., 3.]), array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket        Qobj data =        [[-0.70710678+0.j ]         [ 0. -0.70710678j]] ,        Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket        Qobj data =        [[-0.70710678+0.j ]         [ 0. +0.70710678j]] ],       dtype=object)) >>> ( 1 j * A ) . expm () # 演算子の行列指数Quantum オブジェクト: dims = [[2], [2]]、shape = (2, 2)、type = oper、isherm = False Qobj data = [[-0.2248451-0.35017549j -0.4912955-0.7651474j ] [ 0.4912955+0.7651474j -0.2248451-0.35017549j]] >>> qutip . tensor ( qutip . sigmaz ()、qutip . sigmay ()) # テンソル積 量子オブジェクト: dims = [[2, 2], [2, 2]]、shape = (4, 4)、type = oper、isherm = True Qobj data = [[0.+0.j 0.-1.j 0.+ 0.j 0.+0.j] [0.+1.j 0.+0.j 0.+0.j 0.+0.j] [0.+0.j 0.+0.j 0.+0.j 0.+1.j] [0.+0.j 0.+0.j 0.-1.j 0.+0.j]]
 









   




  

>>> Hamiltonian  =  qutip.sigmay () >>> times = np.linspace ( 0,2,10 ) >>> result = qutip.sesolve ( Hamiltonian , psi , times , [ psi.proj ( ), phi.proj ()]) #シュレーディンガー方程式に従ったシステムのユニタリ時間発展>>> expectpsi , expectphi = result.expect # psiとphiへの射影子の期待値>>> plt.figure ( dpi = 200 ) >>> plt.plot ( times , expectpsi ) >>> plt.plot ( times , expectphi ) >>> plt.legend ( [ r " $ \ psi $ " , r " $ \ phi $ " ] ) >>> plt.show ( )