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

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from symengine import pi

import mimiqcircuits as mc


[docs] def GateS(): 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> """ return mc.Power(mc.GateZ(), 1 / 2)
mc.register_power_alias(mc.GateZ, 1 / 2, "S") @mc.register_power_decomposition(mc.GateZ, 1 / 2) def _decompose_gates(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateU(0, 0, pi / 2), q) return circ
[docs] def GateSDG(): 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> """ return mc.Inverse(GateS())
@mc.register_inverse_decomposition((mc.Power, mc.GateZ, 1 / 2)) def _decompose_gatesdg(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateU(0, 0, -pi / 2), q) return circ