def _represent_ZGate(self, basis, **options):
"""
Represents the (I)QFT In the Z Basis
"""
nqubits = options.get('nqubits',0)
if nqubits == 0:
raise QuantumError('The number of qubits must be given as nqubits.')
if nqubits < self.min_qubits:
raise QuantumError(
'The number of qubits %r is too small for the gate.' % nqubits
)
size = self.size
omega = self.omega
#Make a matrix that has the basic Fourier Transform Matrix
arrayFT = [[omega**(i*j%size)/sqrt(size) for i in range(size)] for j in range(size)]
matrixFT = Matrix(arrayFT)
#Embed the FT Matrix in a higher space, if necessary
if self.label[0] != 0:
matrixFT = matrix_tensor_product(eye(2**self.label[0]), matrixFT)
if self.min_qubits < nqubits:
matrixFT = matrix_tensor_product(matrixFT, eye(2**(nqubits-self.min_qubits)))
return matrixFT
def _represent_ZGate(self, basis, **options):
"""
Represents the (I)QFT In the Z Basis
"""
nqubits = options.get('nqubits',0)
if nqubits == 0:
raise QuantumError('The number of qubits must be given as nqubits.')
if nqubits < self.min_qubits:
raise QuantumError(
'The number of qubits %r is too small for the gate.' % nqubits
)
size = self.size
omega = self.omega
#Make a matrix that has the basic Fourier Transform Matrix
arrayFT = [[omega**(i*j%size)/sqrt(size) for i in range(size)] for j in range(size)]
matrixFT = Matrix(arrayFT)
#Embed the FT Matrix in a higher space, if necessary
if self.label[0] != 0:
matrixFT = matrix_tensor_product(eye(2**self.label[0]), matrixFT)
if self.min_qubits < nqubits:
matrixFT = matrix_tensor_product(matrixFT, eye(2**(nqubits-self.min_qubits)))
return matrixFT
def matrix_eye(n, **options):
"""Get the version of eye and tensor_product for a given format."""
format = options.get('format', 'sympy')
if format == 'sympy':
return matrices.eye(n)
elif format == 'numpy':
return _numpy_eye(n)
elif format == 'scipy.sparse':
return _scipy_sparse_eye(n)
raise NotImplementedError('Invalid format: %r' % format)
def matrix_eye(n, **options):
"""Get the version of eye and tensor_product for a given format."""
format = options.get('format','sympy')
if format == 'sympy':
return matrices.eye(n)
elif format == 'numpy':
return _numpy_eye(n)
elif format == 'scipy.sparse':
return _scipy_sparse_eye(n)
raise NotImplementedError('Invalid format: %r' % format)
def scale(x, y, pt=None):
"""Return the matrix to multiply a 2-D point's coordinates by x and y.
If pt is given, the scaling is done relative to that point."""
rv = eye(3)
rv[0, 0] = x
rv[1, 1] = y
if pt:
from sympy.geometry.point import Point
pt = Point(pt)
tr1 = translate(*(-pt).args)
tr2 = translate(*pt.args)
return tr1 * rv * tr2
return rv
def scale(x, y, pt=None):
"""Return the matrix to multiply a 2-D point's coordinates by x and y.
If pt is given, the scaling is done relative to that point."""
rv = eye(3)
rv[0, 0] = x
rv[1, 1] = y
if pt:
from sympy.geometry.point import Point
pt = Point(pt)
tr1 = translate(*(-pt).args)
tr2 = translate(*pt.args)
return tr1*rv*tr2
return rv
def rotate(th):
"""Return the matrix to rotate a 2-D point about the origin by ``angle``.
The angle is measured in radians. To Point a point about a point other
then the origin, translate the Point, do the rotation, and
translate it back:
>>> from sympy.geometry.entity import rotate, translate
>>> from sympy import Point, pi
>>> rot_about_11 = translate(-1, -1)*rotate(pi/2)*translate(1, 1)
>>> Point(1, 1).transform(rot_about_11)
Point(1, 1)
>>> Point(0, 0).transform(rot_about_11)
Point(2, 0)
"""
s = sin(th)
rv = eye(3)*cos(th)
rv [0, 1] = s
rv[1, 0] = -s
rv[2, 2] = 1
return rv
def rotate(th):
"""Return the matrix to rotate a 2-D point about the origin by ``angle``.
The angle is measured in radians. To Point a point about a point other
then the origin, translate the Point, do the rotation, and
translate it back:
>>> from sympy.geometry.entity import rotate, translate
>>> from sympy import Point, pi
>>> rot_about_11 = translate(-1, -1)*rotate(pi/2)*translate(1, 1)
>>> Point(1, 1).transform(rot_about_11)
Point(1, 1)
>>> Point(0, 0).transform(rot_about_11)
Point(2, 0)
"""
s = sin(th)
rv = eye(3) * cos(th)
rv[0, 1] = s
rv[1, 0] = -s
rv[2, 2] = 1
return rv
def scale(x, y):
"""Return the matrix to multiply a 2-D point's coordinates by x and y."""
rv = eye(3)
rv[0, 0] = x
rv[1, 1] = y
return rv
def translate(x, y):
"""Return the matrix to translate a 2-D point by x and y."""
rv = eye(3)
rv[2, 0] = x
rv[2, 1] = y
return rv
def translate(x, y):
"""Return the matrix to translate a 2-D point by x and y."""
rv = eye(3)
rv[2, 0] = x
rv[2, 1] = y
return rv