def _partial_transpose_sparse(rho, mask):
"""
Implement the partial transpose using the CSR sparse matrix.
"""
data = sp.lil_matrix((rho.shape[0], rho.shape[1]), dtype=complex)
for m in range(len(rho.data.indptr) - 1):
n1 = rho.data.indptr[m]
n2 = rho.data.indptr[m + 1]
psi_A = state_index_number(rho.dims[0], m)
for idx, n in enumerate(rho.data.indices[n1:n2]):
psi_B = state_index_number(rho.dims[1], n)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
data[m_pt, n_pt] = rho.data.data[n1 + idx]
return Qobj(data.tocsr(), dims=rho.dims)
def _partial_transpose_sparse(rho, mask):
"""
Implement the partial transpose using the CSR sparse matrix.
"""
data = sp.lil_matrix((rho.shape[0], rho.shape[1]), dtype=complex)
for m in range(len(rho.data.indptr) - 1):
n1 = rho.data.indptr[m]
n2 = rho.data.indptr[m + 1]
psi_A = state_index_number(rho.dims[0], m)
for idx, n in enumerate(rho.data.indices[n1:n2]):
psi_B = state_index_number(rho.dims[1], n)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
data[m_pt, n_pt] = rho.data.data[n1 + idx]
return Qobj(data.tocsr(), dims=rho.dims)
def update_rho(self, rho):
"""
calculate probability distribution for quadrature measurement
outcomes given a two-mode density matrix
"""
X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1])
p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
N = rho.dims[0][0]
M1 = np.zeros((N, N, len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
M2 = np.zeros((N, N, len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
for m in range(N):
for n in range(N):
M1[m,n] = exp(-1j * self.theta1 * (m - n)) / \
sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \
exp(-X1 ** 2) * np.polyval(hermite(m), X1) * np.polyval(hermite(n), X1)
M2[m,n] = exp(-1j * self.theta2 * (m - n)) / \
sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \
exp(-X2 ** 2) * np.polyval(hermite(m), X2) * np.polyval(hermite(n), X2)
for n1 in range(N):
for n2 in range(N):
i = state_number_index([N, N], [n1, n2])
for p1 in range(N):
for p2 in range(N):
j = state_number_index([N, N], [p1, p2])
p += M1[n1, p1] * M2[n2, p2] * rho.data[i, j]
self.data = p
def swap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(swap(), N, control, target)
else:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Q
def swap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(swap(), N, control, target)
else:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Q
def iswap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the iSWAP gate.
Returns
-------
iswap_gate : qobj
Quantum object representation of iSWAP gate
Examples
--------
>>> iswap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = False
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+1.j 0.+0.j]
[ 0.+0.j 0.+1.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N), dtype=complex)
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
val = 1.0
else:
s2 = s1.copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
val = 1.0j
data[i1, i2] = val
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(iswap(), N, control, target)
else:
return Qobj(array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0],
[0, 0, 0, 1]]),
dims=[[2, 2], [2, 2]])
def iswap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the iSWAP gate.
Returns
-------
iswap_gate : qobj
Quantum object representation of iSWAP gate
Examples
--------
>>> iswap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = False
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+1.j 0.+0.j]
[ 0.+0.j 0.+1.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N), dtype=complex)
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
val = 1.0
else:
s2 = s1.copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
val = 1.0j
data[i1, i2] = val
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(iswap(), N, control, target)
else:
return Qobj(array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0],
[0, 0, 0, 1]]),
dims=[[2, 2], [2, 2]])
def swap(mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Qobj(Q)
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
def swap(mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Qobj(Q)
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
def iswap(mask=None):
"""Quantum object representing the iSWAP gate.
Returns
-------
iswap_gate : qobj
Quantum object representation of iSWAP gate
Examples
--------
>>> iswap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = False
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+1.j 0.+0.j]
[ 0.+0.j 0.+1.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
return Qobj(array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0],
[0, 0, 0, 1]]),
dims=[[2, 2], [2, 2]])
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N), dtype=complex)
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
val = 1.0
else:
s2 = s1.copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
val = 1.0j
data[i1, i2] = val
return Qobj(data, dims=[dims, dims], shape=[N, N])
def iswap(mask=None):
"""Quantum object representing the iSWAP gate.
Returns
-------
iswap_gate : qobj
Quantum object representation of iSWAP gate
Examples
--------
>>> iswap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = False
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+1.j 0.+0.j]
[ 0.+0.j 0.+1.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
return Qobj(array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0],
[0, 0, 0, 1]]),
dims=[[2, 2], [2, 2]])
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N), dtype=complex)
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
val = 1.0
else:
s2 = s1.copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
val = 1.0j
data[i1, i2] = val
return Qobj(data, dims=[dims, dims], shape=[N, N])
def _partial_transpose_reference(rho, mask):
"""
This is a reference implementation that explicitly loops over
all states and performs the transpose. It's slow but easy to
understand and useful for testing.
"""
A_pt = np.zeros(rho.shape, dtype=complex)
for psi_A in state_number_enumerate(rho.dims[0]):
m = state_number_index(rho.dims[0], psi_A)
for psi_B in state_number_enumerate(rho.dims[1]):
n = state_number_index(rho.dims[1], psi_B)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
A_pt[m_pt, n_pt] = rho.data[m, n]
return Qobj(A_pt, dims=rho.dims)
def _partial_transpose_reference(rho, mask):
"""
This is a reference implementation that explicitly loops over
all states and performs the transpose. It's slow but easy to
understand and useful for testing.
"""
A_pt = np.zeros(rho.shape, dtype=complex)
for psi_A in state_number_enumerate(rho.dims[0]):
m = state_number_index(rho.dims[0], psi_A)
for psi_B in state_number_enumerate(rho.dims[1]):
n = state_number_index(rho.dims[1], psi_B)
m_pt = state_number_index(
rho.dims[1], np.choose(mask, [psi_A, psi_B]))
n_pt = state_number_index(
rho.dims[0], np.choose(mask, [psi_B, psi_A]))
A_pt[m_pt, n_pt] = rho.data[m, n]
return Qobj(A_pt, dims=rho.dims)
def update_rho(self, rho):
"""
calculate probability distribution for quadrature measurement
outcomes given a two-mode density matrix
"""
X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1])
p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
N = rho.dims[0][0]
M1 = np.zeros((N, N, len(self.xvecs[0]), len(self.xvecs[1])),
dtype=complex)
M2 = np.zeros((N, N, len(self.xvecs[0]), len(self.xvecs[1])),
dtype=complex)
for m in range(N):
for n in range(N):
M1[m, n] = exp(-1j * self.theta1 * (m - n)) / \
sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \
exp(-X1 ** 2) * np.polyval(
hermite(m), X1) * np.polyval(hermite(n), X1)
M2[m, n] = exp(-1j * self.theta2 * (m - n)) / \
sqrt(pi * 2 ** (m + n) * factorial(n) * factorial(m)) * \
exp(-X2 ** 2) * np.polyval(
hermite(m), X2) * np.polyval(hermite(n), X2)
for n1 in range(N):
for n2 in range(N):
i = state_number_index([N, N], [n1, n2])
for p1 in range(N):
for p2 in range(N):
j = state_number_index([N, N], [p1, p2])
p += M1[n1, p1] * M2[n2, p2] * rho.data[i, j]
self.data = p
def update_psi(self, psi):
"""
calculate probability distribution for quadrature measurement
outcomes given a two-mode wavefunction
"""
X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1])
p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
N = psi.dims[0][0]
for n1 in range(N):
kn1 = exp(-1j * self.theta1 * n1) / \
sqrt(sqrt(pi) * 2 ** n1 * factorial(n1)) * \
exp(-X1 ** 2 / 2.0) * np.polyval(hermite(n1), X1)
for n2 in range(N):
kn2 = exp(-1j * self.theta2 * n2) / \
sqrt(sqrt(pi) * 2 ** n2 * factorial(n2)) * \
exp(-X2 ** 2 / 2.0) * np.polyval(hermite(n2), X2)
i = state_number_index([N, N], [n1, n2])
p += kn1 * kn2 * psi.data[i, 0]
self.data = abs(p)**2
def update_psi(self, psi):
"""
calculate probability distribution for quadrature measurement
outcomes given a two-mode wavefunction
"""
X1, X2 = np.meshgrid(self.xvecs[0], self.xvecs[1])
p = np.zeros((len(self.xvecs[0]), len(self.xvecs[1])), dtype=complex)
N = psi.dims[0][0]
for n1 in range(N):
kn1 = exp(-1j * self.theta1 * n1) / \
sqrt(sqrt(pi) * 2 ** n1 * factorial(n1)) * \
exp(-X1 ** 2 / 2.0) * np.polyval(hermite(n1), X1)
for n2 in range(N):
kn2 = exp(-1j * self.theta2 * n2) / \
sqrt(sqrt(pi) * 2 ** n2 * factorial(n2)) * \
exp(-X2 ** 2 / 2.0) * np.polyval(hermite(n2), X2)
i = state_number_index([N, N], [n1, n2])
p += kn1 * kn2 * psi.data[i, 0]
self.data = abs(p) ** 2
