"""This module implements the PDGate."""
from __future__ import annotations
from openqudit.expressions import UnitaryExpression as _UnitaryExpression
from bqskit.ir.gates.quditgate import QuditGate
from bqskit.utils.cachedclass import CachedClass
from bqskit.utils.typing import is_integer
[docs]
class PDGate(QuditGate, CachedClass):
"""
The one-qudit P[i] gate.
The clock gate is given by the following formula:
.. math::
P[i]_d = \\sum_{j} (-\\omega^2)^{\\delta_{ij}} |j\\rangle\\langle j|
where
.. math::
\\omega = \\exp(\\frac{2\\pi i}{d})
and d is the number of levels (2 levels is a qubit,
3 levels is a qutrit, etc.)
References:
- https://pubs.aip.org/aip/jmp/article-abstract/56/3/032202/763827
"""
_num_qudits = 1
_num_params = 0
[docs]
def __init__(self, index: int, radix: int = 3) -> None:
"""
Construct a PDGate.
Args:
index (int): The level for the phase qudit gate (<radix).
radix (int): The number of qudit levels (>=2). Defaults to
qutrits.
Raises:
ValueError: if radix < 2
ValueError: if index >= radix
"""
if not is_integer(radix):
raise TypeError(f'Expected integer for radix, got {type(radix)}.')
if radix < 2:
raise ValueError(f'Radix must be greater than 1, got {radix}.')
if not is_integer(index):
raise TypeError(f'Expected integer for index, got {type(index)}.')
if index < 0 or index >= radix:
raise ValueError(
'PDGate index must be less radix and above 0:'
f'got: {index=}; {radix=}.',
)
self._radix = radix
self.index = index
diag = '~e^(i*4*%d*π/%d)' % (index, radix)
rows = [
'[' + ','.join(
(diag if r == index else '1') if r == c else '0'
for c in range(radix)
) + ']'
for r in range(radix)
]
self._expr = _UnitaryExpression(
'PD%d_%d<%d>() { [%s] }' % (index, radix, radix, ','.join(rows)),
)