def phase_fac(ang_rads, lib='np'):
"""
Returns
exp(1j*ang_rads*I_2) = [[x, 0],[0, x]] with x = exp(1j*ang_rads)
Parameters
----------
ang_rads : float
lib : str
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0.] * 4
tlist[0] = ang_rads
return pu2(*tlist)
mat_dict = OneBitGates.const_dict(0)
x = OneBitGates.get_fun(lib, 'exp')(1j * ang_rads)
mat_dict['11'] = x
mat_dict['00'] = x
return OneBitGates.get_mat(lib, mat_dict)
def u2(rads0, rads1, rads2, rads3, lib='np'):
"""
Returns arbitrary 2-dim unitary matrix (U(2) group) parametrized as
follows:
exp(1j*(rads0 + rads1*sig_x + rads2*sig_y + rads3*sig_z))
where rads1 is an angle in radians and sig_x is the x Pauli
matrix, etc.
Parameters
----------
rads0 : float
rads1 : float
rads2 : float
rads3 : float
lib : str
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [rads0, rads1, rads2, rads3]
return pu2(*tlist)
return OneBitGates.get_fun(lib, 'exp')(1j * rads0) * \
OneBitGates.rot(rads1, rads2, rads3, lib=lib)
def u2(rads0, rads1, rads2, rads3):
"""
Returns arbitrary 2-dim unitary matrix (U(2) group) parametrized as
follows:
exp(1j*(rads0 + rads1*sig_x + rads2*sig_y + rads3*sig_z))
where rads1 is an angle in radians and sig_x is the x Pauli
matrix, etc.
Parameters
----------
rads0 : float
rads1 : float
rads2 : float
rads3 : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [rads0, rads1, rads2, rads3]
return pu2(*tlist)
return np.exp(1j*rads0)*OneBitGates.rot(rads1, rads2, rads3)
def P_0_phase_fac(ang_rads):
"""
Returns
exp(1j*ang_rads*P_0) = [[x, 0],[0, 1]] with x = exp(1j*ang_rads)
Parameters
----------
ang_rads : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0.]*4
tlist[0] = ang_rads/2
tlist[3] = ang_rads/2
return np.exp(1j*ang_rads/2)*pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
mat[0, 0] = np.exp(1j*ang_rads)
mat[1, 1] = 1
return mat
def phase_fac(ang_rads):
"""
Returns
exp(1j*ang_rads*I_2) = [[x, 0],[0, x]] with x = exp(1j*ang_rads)
Parameters
----------
ang_rads : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0.]*4
tlist[0] = ang_rads
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
x = np.exp(1j*ang_rads)
mat[1, 1] = x
mat[0, 0] = x
return mat
def P_0_phase_fac(ang_rads):
"""
Returns
exp(1j*ang_rads*P_0) = [[x, 0],[0, 1]] with x = exp(1j*ang_rads)
Parameters
----------
ang_rads : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0.] * 4
tlist[0] = ang_rads / 2
tlist[3] = ang_rads / 2
return np.exp(1j * ang_rads / 2) * pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
mat[0, 0] = np.exp(1j * ang_rads)
mat[1, 1] = 1
return mat
def phase_fac(ang_rads):
"""
Returns
exp(1j*ang_rads*I_2) = [[x, 0],[0, x]] with x = exp(1j*ang_rads)
Parameters
----------
ang_rads : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0.] * 4
tlist[0] = ang_rads
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
x = np.exp(1j * ang_rads)
mat[1, 1] = x
mat[0, 0] = x
return mat
def rot_ax(rad_ang, axis, lib='np'):
"""
Returns
exp(1j*rad_ang*sig_n)
where n = x if axis = 1, n = y if axis = 2 and n = z if axis = 3
Parameters
----------
rad_ang : float
axis : int
lib : str
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
assert axis in [1, 2, 3]
tlist = [0.] * 4
tlist[axis] = rad_ang
# print('mmbbvv', axis, pu2(*tlist))
return pu2(*tlist)
mat_dict = OneBitGates.const_dict(0)
c = OneBitGates.get_fun(lib, 'cos')(rad_ang)
s = OneBitGates.get_fun(lib, 'sin')(rad_ang)
if axis == 1:
mat_dict['00'] = c
mat_dict['01'] = 1j * s
mat_dict['10'] = 1j * s
mat_dict['11'] = c
elif axis == 2:
mat_dict['00'] = c
mat_dict['01'] = s
mat_dict['10'] = -s
mat_dict['11'] = c
elif axis == 3:
mat_dict['00'] = c + 1j * s
mat_dict['11'] = c - 1j * s
else:
assert False, "axis not in [1,2,3]"
return OneBitGates.get_mat(lib, mat_dict)
def rot_ax(rad_ang, axis):
"""
Returns
exp(1j*rad_ang*sig_n)
where n = x if axis = 1, n = y if axis = 2 and n = z if axis = 3
Parameters
----------
rad_ang : float
axis : int
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
assert axis in [1, 2, 3]
tlist = [0.]*4
tlist[axis] = rad_ang
# print('mmbbvv', axis, pu2(*tlist))
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
c = np.cos(rad_ang)
s = np.sin(rad_ang)
if axis == 1:
mat[0, 0] = c
mat[0, 1] = 1j*s
mat[1, 0] = 1j*s
mat[1, 1] = c
elif axis == 2:
mat[0, 0] = c
mat[0, 1] = s
mat[1, 0] = -s
mat[1, 1] = c
elif axis == 3:
mat[0, 0] = c + 1j*s
mat[1, 1] = c - 1j*s
else:
assert False, "axis not in [1,2,3]"
return mat
def rot_ax(rad_ang, axis):
"""
Returns
exp(1j*rad_ang*sig_n)
where n = x if axis = 1, n = y if axis = 2 and n = z if axis = 3
Parameters
----------
rad_ang : float
axis : int
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
assert axis in [1, 2, 3]
tlist = [0.] * 4
tlist[axis] = rad_ang
# print('mmbbvv', axis, pu2(*tlist))
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
c = np.cos(rad_ang)
s = np.sin(rad_ang)
if axis == 1:
mat[0, 0] = c
mat[0, 1] = 1j * s
mat[1, 0] = 1j * s
mat[1, 1] = c
elif axis == 2:
mat[0, 0] = c
mat[0, 1] = s
mat[1, 0] = -s
mat[1, 1] = c
elif axis == 3:
mat[0, 0] = c + 1j * s
mat[1, 1] = c - 1j * s
else:
assert False, "axis not in [1,2,3]"
return mat
def rot(rad_ang_x, rad_ang_y, rad_ang_z, lib='np'):
"""
Returns
exp(1j*(rad_ang_x*sig_x + rad_ang_y*sig_y + rad_ang_z*sig_z))
where rad_ang_x is an angle in radians and sig_x is the x Pauli
matrix, etc.
Parameters
----------
rad_ang_x : float
rad_ang_y : float
rad_ang_z : float
lib : str
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0., rad_ang_x, rad_ang_y, rad_ang_z]
return pu2(*tlist)
mat_dict = OneBitGates.const_dict(0)
vec = [rad_ang_x, rad_ang_y, rad_ang_z]
n = OneBitGates.get_fun(lib, 'sqrt')(vec[0]**2 + vec[1]**2 + vec[2]**2)
if abs(n) < 1e-8:
mat_dict['00'] = 1
mat_dict['11'] = 1
else:
nx = rad_ang_x / n
ny = rad_ang_y / n
nz = rad_ang_z / n
c = OneBitGates.get_fun(lib, 'cos')(n)
s = OneBitGates.get_fun(lib, 'sin')(n)
mat_dict['00'] = c + 1j * s * nz
mat_dict['01'] = s * ny + 1j * s * nx
mat_dict['10'] = -s * ny + 1j * s * nx
mat_dict['11'] = c - 1j * s * nz
return OneBitGates.get_mat(lib, mat_dict)
def rot(rad_ang_x, rad_ang_y, rad_ang_z):
"""
Returns
exp(1j*(rad_ang_x*sig_x + rad_ang_y*sig_y + rad_ang_z*sig_z))
where rad_ang_x is an angle in radians and sig_x is the x Pauli
matrix, etc.
Parameters
----------
rad_ang_x : float
rad_ang_y : float
rad_ang_z : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0., rad_ang_x, rad_ang_y, rad_ang_z]
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
vec = np.array([rad_ang_x, rad_ang_y, rad_ang_z])
n = np.linalg.norm(vec) # sqrt(dot(vec, vec.conj))
if abs(n) < 1e-8:
mat[0, 0] = 1
mat[1, 1] = 1
else:
nx = rad_ang_x/n
ny = rad_ang_y/n
nz = rad_ang_z/n
c = np.cos(n)
s = np.sin(n)
mat[0, 0] = c + 1j*s*nz
mat[0, 1] = s*ny + 1j*s*nx
mat[1, 0] = -s*ny + 1j*s*nx
mat[1, 1] = c - 1j*s*nz
return mat
def rot(rad_ang_x, rad_ang_y, rad_ang_z):
"""
Returns
exp(1j*(rad_ang_x*sig_x + rad_ang_y*sig_y + rad_ang_z*sig_z))
where rad_ang_x is an angle in radians and sig_x is the x Pauli
matrix, etc.
Parameters
----------
rad_ang_x : float
rad_ang_y : float
rad_ang_z : float
Returns
-------
np.ndarray
"""
if 'autograd.numpy' in sys.modules:
tlist = [0., rad_ang_x, rad_ang_y, rad_ang_z]
return pu2(*tlist)
ty = np.complex128
mat = np.zeros([2, 2], dtype=ty)
vec = np.array([rad_ang_x, rad_ang_y, rad_ang_z])
n = np.linalg.norm(vec) # sqrt(dot(vec, vec.conj))
if abs(n) < 1e-8:
mat[0, 0] = 1
mat[1, 1] = 1
else:
nx = rad_ang_x / n
ny = rad_ang_y / n
nz = rad_ang_z / n
c = np.cos(n)
s = np.sin(n)
mat[0, 0] = c + 1j * s * nz
mat[0, 1] = s * ny + 1j * s * nx
mat[1, 0] = -s * ny + 1j * s * nx
mat[1, 1] = c - 1j * s * nz
return mat
