# weylchamber.cartan_decomposition module¶

## Summary¶

Functions:

 cartan_decomposition 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. Tuple[Qobj, Qobj, Qobj] 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)