weylchamber.cartan_decomposition module¶
Summary¶
Functions:
Calculate the Cartan Decomposition of the given U in U(4) |
__all__
: cartan_decomposition
Reference¶
- weylchamber.cartan_decomposition.cartan_decomposition(U)[source]¶
Calculate the Cartan Decomposition of the given U in U(4)
\[\Op{U} = \Op{k}_1 \Op{A} \Op{k}_2\]up to a global phase factor \((\det \Op{U})^{\frac{1}{4}}\).
- Parameters
U (
Union
[Qobj
,ndarray
]) – Two-qubit quantum gate. Must be unitary.- Return type
Tuple
[Qobj
,Qobj
,Qobj
]- Returns
tuple \((\Op{k}_1, \Op{A}, \Op{k}_2)\) where \(\Op{k}_1\) is the left local operations in SU(2) x SU(2), \(\Op{A}\) is non-local operations, in SU(4), and \(\Op{k}_2\) is the right local operations in SU(2) x SU(2).
Notes
If you are working with a logical subspace, you should unitarize U before calculating the Cartan decomposition
References
D. Reich. Optimising the nonlocal content of a two-qubit gate. Diploma Thesis. FU Berlin, 2010. Appendix E
Zhang et al. PRA 67, 042313 (2003)