Description
Feature details
In the following lie_closure code, there are many redundant combinations that are checked:
for ps1, ps2 in itertools.combinations(vspace.basis, 2):
com = ps1.commutator(ps2)
com.simplify()
The issue is that we do not need to always check all combinations from vspace.basis; many have been checked in previous epochs. As a simple example, if our basis is {A,B} and we find a linearly independent C = [A,B] in an epoch, we do not need to check [A,B] again.
Instead, we only need to take the commutation of an operator in the original generator set and one from the most recent epoch. See algorithm 1 in this paper:
Implementation
Here is an attempt at updating the code. Note the new variables orig, S_prev, and S_new in particular. In addition to checking if len(com) == 0, we also should check if not vspace.is_independent(com). It seems that add also does an independence check.
def lie_closure(
generators: Iterable[Union[PauliWord, PauliSentence, Operator]],
max_iterations: int = 10000,
verbose: bool = False,
pauli: bool = False,
tol: float = None,
) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
if not all(isinstance(op, (PauliSentence, PauliWord)) for op in generators):
if pauli:
raise TypeError(
"All generators need to be of type PauliSentence or PauliWord when using pauli=True in lie_closure."
)
generators = [
rep if (rep := op.pauli_rep) is not None else qml.pauli.pauli_sentence(op)
for op in generators
]
orig = PauliVSpace(generators, tol=tol)
S_prev = PauliVSpace(generators, tol=tol)
vspace = PauliVSpace(generators, tol=tol)
epoch = 0
new_length = len(vspace)
while (new_length > 0) and (epoch < max_iterations):
if verbose:
print(f"epoch {epoch+1} of lie_closure, DLA size is {len(vspace.basis)}")
S_new = PauliVSpace([], tol=tol)
for ps1 in orig.basis:
for ps2 in S_prev.basis:
com = ps1.commutator(ps2)
com.simplify()
if len(com) == 0: # skip because operators commute
continue
# result is always purely imaginary
# remove common factor 2 with Pauli commutators
for pw, val in com.items():
com[pw] = val.imag / 2
if not vspace.is_independent(com):
continue
vspace.add(com, tol=tol)
S_new.add(com, tol=tol)
# Updated number of linearly independent PauliSentences from previous and current step
new_length = len(S_new)
S_prev = S_new
epoch += 1
if epoch == max_iterations:
warnings.warn(f"reached the maximum number of iterations {max_iterations}", UserWarning)
if verbose > 0:
print(f"After {epoch} epochs, reached a DLA size of {len(vspace)}")
res = vspace.basis
if not pauli:
res = [op.operation() for op in res]
return res
How important would you say this feature is?
1: Not important. Would be nice to have.
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