Source code for mimiqcircuits.operations.gates.standard.sx

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from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from symengine import pi


[docs] class GateSX(mc.Power): r"""Single qubit :math:`\sqrt{X}` gate. **Matrix representation:** .. math:: \sqrt{\operatorname{X}} = \frac{1}{2} \begin{pmatrix} 1+i & 1-i \\ 1-i & 1+i\\ \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateSX() SX >>> GateSX().matrix() [0.5 + 0.5*I, 0.5 - 0.5*I] [0.5 - 0.5*I, 0.5 + 0.5*I] <BLANKLINE> >>> c = Circuit().push(GateSX(), 0) >>> c 1-qubit circuit with 1 instructions: └── SX @ q[0] <BLANKLINE> >>> GateSX().power(2), GateSX().inverse() (X, SX†) >>> GateSX().decompose() 1-qubit circuit with 4 instructions: ├── S† @ q[0] ├── H @ q[0] ├── S† @ q[0] └── U(0, 0, 0, (1/4)*pi) @ q[0] <BLANKLINE> """ _name = "SX" name = "SX" def __init__(self): super().__init__(mc.GateX(), 1 / 2)
[docs] def inverse(self): return GateSXDG()
[docs] def isopalias(self): return True
def _control(self, n): return control_one_defined(n, self, mc.GateCSX()) def _power(self, p): # SX * SX = X if p % 4 == 2: return mc.GateX() # (SX * SX) * (SX * SX) = X * X = ID if p % 4 == 0: return mc.GateID() # (SX * SX * SX) * SX = ID => SX * SX * SX = SX† if p % 4 == 3: return mc.GateSXDG() # SX * SX * SX * SX = ID => SX^(n*4) * SX = ID * SX = SX if p % 4 == 1: return self return mc.Power(self, p) def __str__(self): return f"{self.name}" def _decompose(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateSDG(), q) circ.push(mc.GateH(), q) circ.push(mc.GateSDG(), q) circ.push(mc.GateU(0, 0, 0, pi / 4), q) return circ
[docs] class GateSXDG(mc.Inverse): r"""Single qubit :math:`\sqrt{X}^\dagger` gate (conjugate transpose of the :math:`\sqrt{X}` gate). **Matrix representation:** .. math:: \sqrt{\operatorname{X}}^\dagger = \frac{1}{2} \begin{pmatrix} 1-i & 1+i \\ 1+i & 1-i\\ \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateSXDG() SX† >>> GateSXDG().matrix() [0.5 - 0.5*I, 0.5 + 0.5*I] [0.5 + 0.5*I, 0.5 - 0.5*I] <BLANKLINE> >>> c = Circuit().push(GateSXDG(), 0) >>> c 1-qubit circuit with 1 instructions: └── SX† @ q[0] <BLANKLINE> >>> GateSXDG().power(2), GateSXDG().inverse() (SX†**2, SX) >>> GateSXDG().decompose() 1-qubit circuit with 4 instructions: ├── S @ q[0] ├── H @ q[0] ├── S @ q[0] └── U(0, 0, 0, (-1/4)*pi) @ q[0] <BLANKLINE> """ def __init__(self): super().__init__(GateSX())
[docs] def inverse(self): return GateSX()
[docs] def isopalias(self): return True
def _control(self, n): return control_one_defined(n, self, mc.GateCSXDG()) def _decompose(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateS(), q) circ.push(mc.GateH(), q) circ.push(mc.GateS(), q) circ.push(mc.GateU(0, 0, 0, -pi / 4), q) return circ