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.

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)