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

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from mimiqcircuits.operations.power import Power
from mimiqcircuits.operations.inverse import Inverse
from mimiqcircuits.operations.gates.standard.pauli import GateZ
from mimiqcircuits.operations.gates.standard.u import GateU
from mimiqcircuits.operations.utils import control_one_defined
import mimiqcircuits as mc
from symengine import pi


[docs] class GateS(Power): r"""Single qubit gate S. It induces a :math:`\frac{\pi}{2}` phase gate. **Matrix representation:** .. math:: \operatorname{S} = \begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateS() S >>> GateS().matrix() [1.0, 0] [0, 0.0 + 1.0*I] <BLANKLINE> >>> c = Circuit().push(GateS(), 0) >>> c 1-qubit circuit with 1 instructions: └── S @ q[0] <BLANKLINE> >>> GateS().power(2), GateS().inverse() (Z, S†) >>> GateS().decompose() 1-qubit circuit with 1 instructions: └── U(0, 0, (1/2)*pi, 0.0) @ q[0] <BLANKLINE> """ _name = "S" def __init__(self): super().__init__(GateZ(), 1 / 2)
[docs] def isopalias(self): return True
[docs] def inverse(self): return GateSDG()
def _power(self, p): pmod = p % 4 # sqrt(S) = T if pmod == 1 / 2: return mc.GateT() # T * T^7 = S^2 * S^2 = Z * Z = ID => T^7 = TDG if pmod == 7 / 2: return mc.GateTDG() # Z^(2n) = ID => S^(4n) = ID if p % 4 == 0: return mc.GateID() # Z^(2n + 1) = Z => S^(4n + 1) = S if p % 4 == 1: return mc.GateS() # S^(4n + 3) = SDG if p % 4 == 3: return mc.GateSDG() # sqrt(Z) = S if p % 2 == 0: return mc.GateZ().power(p / 2) def _control(self, n): return control_one_defined(n, self, mc.GateCS()) def __str__(self): return f"{self.name}" def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(GateU(0, 0, pi / 2), q) return circ
[docs] class GateSDG(Inverse): r"""Single qubit S-dagger gate (conjugate transpose of the S gate). **Matrix representation:** .. math:: \operatorname{S}^\dagger = \begin{pmatrix} 1 & 0 \\ 0 & -i \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateSDG() S† >>> GateSDG().matrix() [1.0, 0] [0, 6.12323399573677e-17 - 1.0*I] <BLANKLINE> >>> c = Circuit().push(GateSDG(), 0) >>> c 1-qubit circuit with 1 instructions: └── S† @ q[0] <BLANKLINE> >>> GateSDG().power(2), GateSDG().inverse() (S†**2, S) >>> GateSDG().decompose() 1-qubit circuit with 1 instructions: └── U(0, 0, (-1/2)*pi, 0.0) @ q[0] <BLANKLINE> """ def __init__(self): super().__init__(GateS())
[docs] def isopalias(self): return True
[docs] def inverse(self): return GateS()
def _control(self, n): return control_one_defined(n, self, mc.GateCSDG()) def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(GateU(0, 0, -pi / 2), q) return circ