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import mimiqcircuits.operations.gates.gate as mcg
from mimiqcircuits.operations.gates.standard.interactions import GateRZX
from mimiqcircuits.operations.utils import power_idempotent
from mimiqcircuits.operations.gates.standard.pauli import GateX
from symengine import sqrt, I, pi, Matrix
[docs]
class GateECR(mcg.Gate):
r"""Two qubit ECR (echo) gate.
**Matrix representation:**
.. math::
\operatorname{ECR} =\begin{pmatrix}
0 & \frac{1}{\sqrt{2}} & 0 & \frac{i}{\sqrt{2}} \\
\frac{1}{\sqrt{2}} & 0 & \frac{-i}{\sqrt{2}} & 0 \\
0 & \frac{i}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\
\frac{-i}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} & 0
\end{pmatrix}
Examples:
>>> from mimiqcircuits import *
>>> GateECR()
ECR
>>> GateECR().matrix()
[0, 0, 0.707106781186548, 0.0 + 0.707106781186548*I]
[0, 0, 0.0 + 0.707106781186548*I, 0.707106781186548]
[0.707106781186548, -0.0 - 0.707106781186548*I, 0, 0]
[-0.0 - 0.707106781186548*I, 0.707106781186548, 0, 0]
<BLANKLINE>
>>> c = Circuit().push(GateECR(), 0, 1)
>>> c
2-qubit circuit with 1 instructions:
└── ECR @ q[0,1]
<BLANKLINE>
>>> GateECR().power(2), GateECR().inverse()
(⨷ ² ID, ECR)
>>> GateECR().decompose()
2-qubit circuit with 3 instructions:
├── RZX((1/4)*pi) @ q[0,1]
├── X @ q[0]
└── RZX((-1/4)*pi) @ q[0,1]
<BLANKLINE>
"""
_name = "ECR"
_num_qubits = 2
_qregsizes = [2]
def _matrix(self):
return Matrix(
[[0, 0, 1, I], [0, 0, I, 1], [1, -I, 0, 0], [-I, 1, 0, 0]]
) / sqrt(2)
[docs]
def inverse(self):
return self
def _power(self, p):
return power_idempotent(self, p)
def _decompose(self, circ, qubits, bits, zvars):
a, b = qubits
circ.push(GateRZX(pi / 4), a, b)
circ.push(GateX(), a)
circ.push(GateRZX(-pi / 4), a, b)
return circ
