SU2 Rotation#

from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register
from qualtran import QBit, QInt, QUInt, QAny
from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma
from typing import *
import numpy as np
import sympy
import cirq

SU2RotationGate#

Implements an arbitrary SU(2) rotation.

The rotation is represented by the matrix:

\[\begin{split} e^{i \alpha} \begin{pmatrix} e^{i(\lambda + \phi)} \cos(\theta) & e^{i\phi} \sin(\theta) \\ e^{i\lambda} \sin(\theta) & - \cos(\theta) \end{pmatrix} \end{split}\]

Parameters#

  • theta: rotation angle \(\theta\) in the above matrix.

  • phi: phase angle \(\phi\) in the above matrix.

  • lambd: phase angle \(\lambda\) in the above matrix.

  • global_shift: phase angle \(\alpha\), i.e. apply a global phase shift of \(e^{i \alpha}\).

References#

from qualtran.bloqs.basic_gates import SU2RotationGate

Example Instances#

su2_rotation_gate = SU2RotationGate(np.pi / 4, np.pi / 2, np.pi / 2)

hadamard = SU2RotationGate(np.pi / 4, 0, 0)

t_gate = SU2RotationGate(0, 3 * np.pi / 4, 0, -3 * np.pi / 4)

Graphical Signature#

from qualtran.drawing import show_bloqs
show_bloqs([su2_rotation_gate, hadamard, t_gate],
           ['`su2_rotation_gate`', '`hadamard`', '`t_gate`'])

Call Graph#

from qualtran.resource_counting.generalizers import ignore_split_join
su2_rotation_gate_g, su2_rotation_gate_sigma = su2_rotation_gate.call_graph(max_depth=1, generalizer=ignore_split_join)
show_call_graph(su2_rotation_gate_g)
show_counts_sigma(su2_rotation_gate_sigma)
../../_images/6d0acb63a2e1b672e922d9cb454d4633deb96ad02c171186cc983676c38a6f39.svg

Counts totals:

  • GPhase((-1+1.2246467991473532e-16j)): 1

  • Rx(1.5707963267948966): 1

  • Rz(0.0): 2