weylchamber.local_invariants module¶

Summary¶

Functions:

`J_T_LI`	Calculate value of the local-invariants functional
`closest_LI`	Find the closest gate that has the given Weyl chamber coordinates
`g1g2g3`	Calculate local invariants \((g_1, g_3, g_3)\)
`g1g2g3_from_c1c2c3`	Calculate local invariants from the Weyl chamber coordinates

__all__: J_T_LI, closest_LI, g1g2g3, g1g2g3_from_c1c2c3

Reference¶

weylchamber.local_invariants.g1g2g3(U, ndigits=8)[source]¶

Calculate local invariants \((g_1, g_3, g_3)\)

Given a two-qubit gate, calculate local invariants \((g_1, g_2, g_3)\). U must be in the canonical basis. For numerical stability, the resulting values are rounded to the given precision, cf. the ndigits parameter of the built-in round() function.

>>> print("%.2f %.2f %.2f" % g1g2g3(qutip.gates.cnot()))
0.00 0.00 1.00

Return type:	`Tuple`[`float`, `float`, `float`]

weylchamber.local_invariants.g1g2g3_from_c1c2c3(c1, c2, c3, ndigits=8)[source]¶

Calculate local invariants from the Weyl chamber coordinates

Calculate the local invariants \((g_1, g_2, g_3)\) from the Weyl chamber coordinates \((c_1, c_2, c_3)\), in units of π. The result is rounded to the given precision, in order to enhance numerical stability (cf. ndigits parameter of the built-in round() function)

Example

>>> CNOT = qutip.gates.cnot()
>>> print("%.2f %.2f %.2f" % g1g2g3_from_c1c2c3(*c1c2c3(CNOT)))
0.00 0.00 1.00

Return type:	`Tuple`[`float`, `float`, `float`]

weylchamber.local_invariants.J_T_LI(O, U, form='g')[source]¶

Calculate value of the local-invariants functional

Parameters:	O (`Union`[`Qobj`, `ndarray`]) – The optimal gate U (`Union`[`Qobj`, `ndarray`]) – The achieved gate form (str) – form of the functional to use, ‘g’ or ‘c’

weylchamber.local_invariants.closest_LI(U, c1, c2, c3, method='leastsq', limit=1e-06)[source]¶

Find the closest gate that has the given Weyl chamber coordinates

The c1, c2, c3 are given in units of π