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

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import mimiqcircuits.operations.gates.gate as mcg
from mimiqcircuits.operations.utils import power_idempotent, control_one_defined
from mimiqcircuits.operations.gates.standard.phase import GateP
from mimiqcircuits.operations.gates.standard.u import GateU
import mimiqcircuits as mc
from symengine import pi, I, Matrix


[docs] class GateX(mcg.Gate): r""" Single qubit Pauli-X gate. **Matrix representation:** .. math:: \operatorname{X} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateX() X >>> GateX().matrix() [0, 1.0] [1.0, 0] <BLANKLINE> >>> c = Circuit().push(GateX(), 0) >>> c 1-qubit circuit with 1 instructions: └── X @ q[0] <BLANKLINE> >>> GateX().power(2), GateX().inverse() (ID, X) >>> GateX().decompose() 1-qubit circuit with 1 instructions: └── U(pi, 0, pi, 0.0) @ q[0] <BLANKLINE> """ _name = "X" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): pmod = p % 2 # sqrt(X) = SX if pmod == 1 / 2: return mc.GateSX() # SX * SX^3 = X * X = ID => SX^3 = SXDG if pmod == 3 / 2: return mc.GateSXDG() # X^(2n) = ID # X^(2n + 1) = X return power_idempotent(self, p) def _control(self, n): return control_one_defined(n, self, mc.GateCX(), mc.GateCCX(), mc.GateC3X()) def _matrix(self): return Matrix([[0, 1], [1, 0]]) def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(GateU(pi, 0, pi), q) return circ
[docs] class GateY(mcg.Gate): r"""Single qubit Pauli-Y gate. **Matrix representation:** .. math:: \operatorname{Y} = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateY() Y >>> GateY().matrix() [0, -0.0 - 1.0*I] [0.0 + 1.0*I, 0] <BLANKLINE> >>> c = Circuit().push(GateY(), 0) >>> GateY().power(2), GateY().inverse() (ID, Y) >>> GateY().decompose() 1-qubit circuit with 1 instructions: └── U(pi, (1/2)*pi, (1/2)*pi, 0.0) @ q[0] <BLANKLINE> """ _name = "Y" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): # Y^(2n) = ID # Y^(2n + 1) = Y return power_idempotent(self, p) def _control(self, n): return control_one_defined(n, self, mc.GateCY()) def _matrix(self): return Matrix([[0, -I], [I, 0]]) def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(GateU(pi, pi/2, pi/2), q) return circ
[docs] class GateZ(mcg.Gate): r"""Single qubit Pauli-Z gate. **Matrix representation:** .. math:: \operatorname{Z} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateZ() Z >>> GateZ().matrix() [1.0, 0] [0, -1.0] <BLANKLINE> >>> c = Circuit().push(GateZ(), 0) >>> GateZ().power(2), GateZ().inverse() (ID, Z) >>> GateZ().decompose() 1-qubit circuit with 1 instructions: └── P(pi) @ q[0] <BLANKLINE> """ _name = "Z" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): pmod = p % 2 # sqrt(Z) = S if pmod == 1 / 2: return mc.GateS() # S * S^3 = Z * Z = ID => S^3 = SDG if pmod == 3 / 2: return mc.GateSDG() # sqrt(S) = T if pmod == 1 / 4: return mc.GateT() # T * T^7 = S^2 * S^2 = Z * Z = ID => T^7 = TDG if pmod == 7 / 4: return mc.GateTDG() # Z^(2n) = ID # Z^(2n + 1) = Z return power_idempotent(self, p) def _control(self, n): return control_one_defined(n, self, mc.GateCZ()) def _matrix(self): return Matrix([[1, 0], [0, -1]]) def _decompose(self, circ, qubits, bits): q = qubits[0] circ.push(GateP(pi), q) return circ