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

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import mimiqcircuits as mc
from mimiqcircuits.operations.utils import power_idempotent
from mimiqcircuits.operations.utils import control_one_defined
from symengine import pi, sqrt, Matrix, I


[docs] class GateH(mc.Gate): r"""Single qubit Hadamard gate. **Matrix representation:** .. math:: \operatorname{H} = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateH() H >>> GateH().matrix() [0.707106781186548, 0.707106781186548] [0.707106781186548, -0.707106781186548] <BLANKLINE> >>> c = Circuit().push(GateH(), 0) >>> c 1-qubit circuit with 1 instructions: └── H @ q[0] <BLANKLINE> >>> GateH().power(2), GateH().inverse() (ID, H) >>> GateH().decompose() 1-qubit circuit with 1 instructions: └── U((1/2)*pi, 0, pi, 0.0) @ q[0] <BLANKLINE> """ _name = "H" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): # H^(2n) = ID # H^(2n+1) = H return power_idempotent(self, p) def _control(self, n): return control_one_defined(n, self, mc.GateCH(), mc.Control(2, GateH())) def _matrix(self): return Matrix([[1, 1], [1, -1]]) / sqrt(2) def _decompose(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateU(pi / 2, 0, pi), q) return circ
[docs] class GateHXY(mc.Gate): r"""Single qubit HXY gate. **Matrix representation:** .. math:: \operatorname{HXY} = \frac{1}{\sqrt{2}} \begin{pmatrix} 0 & 1 - i \\ 1 + i & 0 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateHXY() HXY >>> GateHXY().matrix() [0, 0.707106781186548 - 0.707106781186548*I] [0.707106781186548 + 0.707106781186548*I, 0] <BLANKLINE> >>> c = Circuit().push(GateHXY(), 0) >>> c 1-qubit circuit with 1 instructions: └── HXY @ q[0] <BLANKLINE> >>> GateHXY().power(2), GateHXY().inverse() (HXY**2, HXY) >>> GateHXY().decompose() 1-qubit circuit with 5 instructions: ├── H @ q[0] ├── Z @ q[0] ├── H @ q[0] ├── S @ q[0] └── U(0, 0, 0, (-1/4)*pi) @ q[0] <BLANKLINE> """ _name = "HXY" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): return mc.Power(GateHXY(), p) def _control(self, n): return control_one_defined(n, self, mc.Control(1, GateHXY())) def _matrix(self): return Matrix([[0, 1-I], [1+I, 0]]) / sqrt(2) def _decompose(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateH(), q) circ.push(mc.GateZ(), q) circ.push(mc.GateH(), q) circ.push(mc.GateS(), q) circ.push(mc.GateU(0, 0, 0, -pi/4), q) return circ
[docs] class GateHYZ(mc.Gate): r"""Single qubit HYZ gate. **Matrix representation:** .. math:: \operatorname{HYZ} = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -i \\ i & -1 \end{pmatrix} Examples: >>> from mimiqcircuits import * >>> GateHYZ() HYZ >>> GateHYZ().matrix() [0.707106781186548, -0.0 - 0.707106781186548*I] [0.0 + 0.707106781186548*I, -0.707106781186548] <BLANKLINE> >>> c = Circuit().push(GateHYZ(), 0) >>> c 1-qubit circuit with 1 instructions: └── HYZ @ q[0] <BLANKLINE> >>> GateHYZ().power(2), GateHYZ().inverse() (HYZ**2, HYZ) >>> GateHYZ().decompose() 1-qubit circuit with 5 instructions: ├── H @ q[0] ├── S @ q[0] ├── H @ q[0] ├── Z @ q[0] └── U(0, 0, 0, (-1/4)*pi) @ q[0] <BLANKLINE> """ _name = "HYZ" _num_qubits = 1 _qregsizes = [1]
[docs] def inverse(self): return self
def _power(self, p): return mc.Power(GateHYZ(), p) def _control(self, n): return control_one_defined( n, self, mc.Control(1, GateHYZ()), mc.Control(2, GateHYZ()) ) def _matrix(self): return Matrix([[1, -I], [I, -1]]) / sqrt(2) def _decompose(self, circ, qubits, bits, zvars): q = qubits[0] circ.push(mc.GateH(), q) circ.push(mc.GateS(), q) circ.push(mc.GateH(), q) circ.push(mc.GateZ(), q) circ.push(mc.GateU(0, 0, 0, -pi/4), q) return circ
[docs] class GateHXZ(mc.Gate): r"""Single qubit HXZ gate (alias for :class:`GateH`). **Matrix representation:** .. math:: \operatorname{H} = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} Examples: The HXZ gate behaves exactly like the Hadamard gate: >>> from mimiqcircuits import * >>> GateHXZ() H >>> GateHXZ().matrix() [0.707106781186548, 0.707106781186548] [0.707106781186548, -0.707106781186548] <BLANKLINE> Adding GateHXZ to a circuit: >>> c = Circuit().push(GateHXZ(), 0) Power and inverse of the gate: >>> GateHXZ().power(2), GateHXZ().inverse() (ID, H) Decomposition of the gate: >>> GateHXZ().decompose() 1-qubit circuit with 1 instructions: └── U((1/2)*pi, 0, pi, 0.0) @ q[0] <BLANKLINE> """ def __new__(self): return GateH()