def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, SparsePauliOp):
other = SparsePauliOp(other)
# Validate composition dimensions and qargs match
self._op_shape.compose(other._op_shape, qargs, front)
if qargs is not None:
x1, z1 = self.paulis.x[:, qargs], self.paulis.z[:, qargs]
else:
x1, z1 = self.paulis.x, self.paulis.z
x2, z2 = other.paulis.x, other.paulis.z
num_qubits = other.num_qubits
# This method is the outer version of `BasePauli.compose`.
# `x1` and `z1` have shape `(self.size, num_qubits)`.
# `x2` and `z2` have shape `(other.size, num_qubits)`.
# `x1[:, no.newaxis]` results in shape `(self.size, 1, num_qubits)`.
# `ar = ufunc(x1[:, np.newaxis], x2)` will be in shape `(self.size, other.size, num_qubits)`.
# So, `ar.reshape((-1, num_qubits))` will be in shape `(self.size * other.size, num_qubits)`.
# Ref: https://numpy.org/doc/stable/user/theory.broadcasting.html
phase = np.add.outer(self.paulis._phase,
other.paulis._phase).reshape(-1)
if front:
q = np.logical_and(x1[:, np.newaxis], z2).reshape((-1, num_qubits))
else:
q = np.logical_and(z1[:, np.newaxis], x2).reshape((-1, num_qubits))
# `np.mod` will be applied to `phase` in `SparsePauliOp.__init__`
phase = phase + 2 * q.sum(axis=1, dtype=np.uint8)
x3 = np.logical_xor(x1[:, np.newaxis], x2).reshape((-1, num_qubits))
z3 = np.logical_xor(z1[:, np.newaxis], z2).reshape((-1, num_qubits))
if qargs is None:
pauli_list = PauliList(BasePauli(z3, x3, phase))
else:
x4 = np.repeat(self.paulis.x, other.size, axis=0)
z4 = np.repeat(self.paulis.z, other.size, axis=0)
x4[:, qargs] = x3
z4[:, qargs] = z3
pauli_list = PauliList(BasePauli(z4, x4, phase))
# note: the following is a faster code equivalent to
# `coeffs = np.kron(self.coeffs, other.coeffs)`
# since `self.coeffs` and `other.coeffs` are both 1d arrays.
coeffs = np.multiply.outer(self.coeffs, other.coeffs).ravel()
return SparsePauliOp(pauli_list, coeffs, copy=False)
def sum(ops):
"""Sum of SparsePauliOps.
This is a specialized version of the builtin ``sum`` function for SparsePauliOp
with smaller overhead.
Args:
ops (list[SparsePauliOp]): a list of SparsePauliOps.
Returns:
SparsePauliOp: the SparsePauliOp representing the sum of the input list.
Raises:
QiskitError: if the input list is empty.
QiskitError: if the input list includes an object that is not SparsePauliOp.
QiskitError: if the numbers of qubits of the objects in the input list do not match.
"""
if len(ops) == 0:
raise QiskitError("Input list is empty")
if not all(isinstance(op, SparsePauliOp) for op in ops):
raise QiskitError(
"Input list includes an object that is not SparsePauliOp")
for other in ops[1:]:
ops[0]._op_shape._validate_add(other._op_shape)
z = np.vstack([op.paulis.z for op in ops])
x = np.vstack([op.paulis.x for op in ops])
phase = np.hstack([op.paulis._phase for op in ops])
pauli_list = PauliList(BasePauli(z, x, phase))
coeffs = np.hstack([op.coeffs for op in ops])
return SparsePauliOp(pauli_list,
coeffs,
ignore_pauli_phase=True,
copy=False)
def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, "qargs", None)
if not isinstance(other, SparsePauliOp):
other = SparsePauliOp(other)
# Validate composition dimensions and qargs match
self._op_shape.compose(other._op_shape, qargs, front)
if qargs is not None:
x1, z1 = self.paulis.x[:, qargs], self.paulis.z[:, qargs]
else:
x1, z1 = self.paulis.x, self.paulis.z
x2, z2 = other.paulis.x, other.paulis.z
num_qubits = other.num_qubits
# This method is the outer version of `BasePauli.compose`.
# `x1` and `z1` have shape `(self.size, num_qubits)`.
# `x2` and `z2` have shape `(other.size, num_qubits)`.
# `x1[:, no.newaxis]` results in shape `(self.size, 1, num_qubits)`.
# `ar = ufunc(x1[:, np.newaxis], x2)` will be in shape `(self.size, other.size, num_qubits)`.
# So, `ar.reshape((-1, num_qubits))` will be in shape `(self.size * other.size, num_qubits)`.
# Ref: https://numpy.org/doc/stable/user/theory.broadcasting.html
phase = np.add.outer(self.paulis._phase,
other.paulis._phase).reshape(-1)
if front:
q = np.logical_and(x1[:, np.newaxis], z2).reshape((-1, num_qubits))
else:
q = np.logical_and(z1[:, np.newaxis], x2).reshape((-1, num_qubits))
phase = np.mod(phase + 2 * np.sum(q, axis=1), 4)
x3 = np.logical_xor(x1[:, np.newaxis], x2).reshape((-1, num_qubits))
z3 = np.logical_xor(z1[:, np.newaxis], z2).reshape((-1, num_qubits))
if qargs is None:
pauli_list = PauliList(BasePauli(z3, x3, phase))
else:
x4 = np.repeat(self.paulis.x, other.size, axis=0)
z4 = np.repeat(self.paulis.z, other.size, axis=0)
x4[:, qargs] = x3
z4[:, qargs] = z3
pauli_list = PauliList(BasePauli(z4, x4, phase))
coeffs = np.kron(self.coeffs, other.coeffs)
return SparsePauliOp(pauli_list, coeffs)