def pad_matrix(matrix, dim, padding):
"""
Fills matrix dimensions with zeros or identity.
"""
if padding == "compsub":
return matrix
elif padding == "wzeros":
zeros = np.zeros([dim, dim])
matrix = scipy_block_diag(matrix, zeros)
elif padding == "fulluni":
identity = np.eye(dim)
matrix = scipy_block_diag(matrix, identity)
return matrix
def perform(self, node, inputs, output_storage, params=None):
dtype = largest_common_dtype(inputs)
if self.sparse:
output_storage[0][0] = sp.sparse.block_diag(
inputs, self.format, dtype)
else:
output_storage[0][0] = scipy_block_diag(*inputs).astype(dtype)
def perform(self, node, inputs, output_storage, params=None):
dtype = largest_common_dtype(inputs)
if self.sparse:
output_storage[0][0] = sp.sparse.block_diag(
inputs, self.format, dtype
)
else:
output_storage[0][0] = scipy_block_diag(*inputs).astype(dtype)
def test_block_diag():
C1 = np.ones((2, 2))
C2 = np.ones((3, 3)) * 2
C3 = np.ones((3, 3)) * 3
C = scipy_block_diag(C1, C2, C3)
C1 = tt.as_tensor_variable(np.ones((2, 2)))
C2 = tt.as_tensor_variable(np.ones((3, 3)) * 2)
C3 = tt.as_tensor_variable(np.ones((3, 3)) * 3)
assert np.allclose(C, lazy_math.block_diag(C1, C2, C3).eval())
def block_diag(self, *mats):
if config.lazy:
N = [mat.shape[0] for mat in mats]
Nsum = tt.sum(N)
res = tt.zeros((Nsum, Nsum), dtype=theano.config.floatX)
n = 0
for mat in mats:
inds = slice(n, n + mat.shape[0])
res = tt.set_subtensor(res[tuple((inds, inds))], mat)
n += mat.shape[0]
return res
else:
return scipy_block_diag(*mats)
def perfect_gate(gates_str: str, index=[0, 1], dims=[2, 2], proj: str = "wzeros"):
"""
Construct an ideal single or two-qubit gate.
Parameters
----------
gates_str: str
Identifier of the gate, i.e. "X90p".
index : list
Indeces of the subspace(s) the gate acts on
dims : list
Dimension of the subspace(s)
proj : str
Option for projection in the case of more than two-level qubits.
Returns
-------
np.array
Ideal representation of the gate.
"""
do_pad_gate = True
# TODO index for now unused
kron_list = []
# for dim in dims:
# kron_list.append(np.eye(dim))
kron_gate = 1
gate_num = 0
# Note that the gates_str has to be explicit for all subspaces
# (and ordered)
for gate_str in gates_str.split(":"):
lvls = dims[gate_num]
if gate_str == "Id":
gate = Id
elif gate_str == "X90p":
gate = X90p
elif gate_str == "X90m":
gate = X90m
elif gate_str == "Xp":
gate = Xp
elif gate_str == "Y90p":
gate = Y90p
elif gate_str == "Y90m":
gate = Y90m
elif gate_str == "Yp":
gate = Yp
elif gate_str == "Z90p":
gate = Z90p
elif gate_str == "Z90m":
gate = Z90m
elif gate_str == "Zp":
gate = Zp
elif gate_str == "CNOT":
lvls2 = dims[gate_num + 1]
NOT = 1j * perfect_gate("Xp", index, [lvls2], proj)
C = perfect_gate("Id", index, [lvls2], proj)
gate = scipy_block_diag(C, NOT)
# We increase gate_num since CNOT is a two qubit gate
for ii in range(2, lvls):
pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "CZ":
lvls2 = dims[gate_num + 1]
Z = 1j * perfect_gate("Zp", index, [lvls2], proj)
C = perfect_gate("Id", index, [lvls2], proj)
gate = scipy_block_diag(C, Z)
# We increase gate_num since CZ is a two qubit gate
for ii in range(2, lvls):
pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "CR":
# TODO: Fix the ideal CNOT construction.
lvls2 = dims[gate_num + 1]
Z = 1j * perfect_gate("Zp", index, [lvls], proj)
X = perfect_gate("Xp", index, [lvls2], proj)
gate = np.kron(Z, X)
gate_num += 1
do_pad_gate = False
elif gate_str == "CR90":
lvls2 = dims[gate_num + 1]
RXp = perfect_gate("X90p", index, [lvls2], proj)
RXm = perfect_gate("X90m", index, [lvls2], proj)
gate = scipy_block_diag(RXp, RXm)
for ii in range(2, lvls):
gate = pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "iSWAP":
# TODO make construction of iSWAP work with superoperator too
lvls2 = dims[gate_num + 1]
if lvls == 2 and lvls2 == 2:
gate = iswap
elif lvls == 3 and lvls2 == 3:
gate = iswap3
gate_num += 1
do_pad_gate = False
else:
print("gate_str must be one of the basic 90 or 180 degree gates.")
print(
"'Id','X90p','X90m','Xp','Y90p',",
"'Y90m','Yp','Z90p','Z90m','Zp', 'CNOT'",
)
return None
if do_pad_gate:
if proj == "compsub":
pass
elif proj == "wzeros":
zeros = np.zeros([lvls - 2, lvls - 2])
gate = scipy_block_diag(gate, zeros)
elif proj == "fulluni":
identity = np.eye(lvls - 2)
gate = scipy_block_diag(gate, identity)
kron_list.append(gate)
gate_num += 1
return np_kron_n(kron_list)
def perfect_gate( # noqa
gates_str: str, index=[0, 1], dims=[2, 2], proj: str = "wzeros"):
"""
Construct an ideal single or two-qubit gate.
Parameters
----------
gates_str: str
Identifier of the gate, i.e. "RX90p".
index : list
Indeces of the subspace(s) the gate acts on
dims : list
Dimension of the subspace(s)
proj : str
Option for projection in the case of more than two-level qubits.
Returns
-------
np.array
Ideal representation of the gate.
"""
do_pad_gate = True
# TODO index for now unused
kron_list = []
# for dim in dims:
# kron_list.append(np.eye(dim))
# kron_gate = 1
gate_num = 0
# Note that the gates_str has to be explicit for all subspaces
# (and ordered)
for gate_str in gates_str.split(":"):
lvls = dims[gate_num]
if gate_str == "Id":
gate = Id
elif gate_str == "RX90p":
gate = RX90p
elif gate_str == "RX90m":
gate = RX90m
elif gate_str == "RXp":
gate = RXp
elif gate_str == "RY90p":
gate = RY90p
elif gate_str == "RY90m":
gate = RY90m
elif gate_str == "RYp":
gate = RYp
elif gate_str == "RZ90p":
gate = RZ90p
elif gate_str == "RZ90m":
gate = RZ90m
elif gate_str == "RZp":
gate = RZp
elif gate_str == "CNOT":
raise NotImplementedError(
"A correct implementation of perfect CNOT is pending, use CRXp now"
)
elif gate_str == "CRXp":
# TODO Should this be CNOT?
lvls2 = dims[gate_num + 1]
NOT = 1j * perfect_gate("RXp", index, [lvls2], proj)
C = perfect_gate("Id", index, [lvls2], proj)
gate = scipy_block_diag(C, NOT)
# We increase gate_num since CNOT is a two qubit gate
for ii in range(2, lvls):
gate = pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "CRZp":
lvls2 = dims[gate_num + 1]
Z = 1j * perfect_gate("RZp", index, [lvls2], proj)
C = perfect_gate("Id", index, [lvls2], proj)
gate = scipy_block_diag(C, Z)
# We increase gate_num since CRZp is a two qubit gate
for ii in range(2, lvls):
gate = pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "CR":
# TODO: Fix the ideal CNOT construction.
lvls2 = dims[gate_num + 1]
Z = 1j * perfect_gate("RZp", index, [lvls], proj)
X = perfect_gate("RXp", index, [lvls2], proj)
gate = np.kron(Z, X)
gate_num += 1
do_pad_gate = False
elif gate_str == "CR90":
lvls2 = dims[gate_num + 1]
RXp_temp = perfect_gate("RX90p", index, [lvls2], proj)
RXm_temp = perfect_gate("RX90m", index, [lvls2], proj)
gate = scipy_block_diag(RXp_temp, RXm_temp)
for ii in range(2, lvls):
gate = pad_matrix(gate, lvls2, proj)
gate_num += 1
do_pad_gate = False
elif gate_str == "iSWAP":
# TODO make construction of iSWAP work with superoperator too
lvls2 = dims[gate_num + 1]
if lvls == 2 and lvls2 == 2:
gate = iswap
elif lvls == 3 and lvls2 == 3:
gate = iswap3
gate_num += 1
do_pad_gate = False
else:
raise KeyError(
"gate_str must be one of the basic 90 or 180 degree gates: 'Id','RX90p','RX90m','RXp','RY90p','RY90m','RYp','RZ90p','RZ90m','RZp', 'CNOT', CRXp, CRZp, CR, CR90, iSWAP"
)
if do_pad_gate:
if proj == "compsub":
pass
elif proj == "wzeros":
zeros = np.zeros([lvls - 2, lvls - 2])
gate = scipy_block_diag(gate, zeros)
elif proj == "fulluni":
identity = np.eye(lvls - 2)
gate = scipy_block_diag(gate, identity)
else:
raise KeyError("proj should be wzeros, compsub or fulluni")
kron_list.append(gate)
gate_num += 1
return np_kron_n(kron_list)
