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Added the ability to control slackness in physicality conditions. #524

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Added the ability to control slackness in physicality conditions. #524

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0755261
Added the ability to control slackness in physicality conditions.
arsalan-motamedi Nov 15, 2024
778ddc1
fixed errors
arsalan-motamedi Nov 15, 2024
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18 changes: 11 additions & 7 deletions mrmustard/lab_dev/states/dm.py
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Original file line number Diff line number Diff line change
Expand Up @@ -49,10 +49,12 @@ class DM(State):

short_name = "DM"

@property
def is_positive(self) -> bool:
def is_positive(self, atol: float = settings.ATOL) -> bool:
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Rather than adding a parameter what if instead we encouraged users to use

with settings(ATOL=1e-8):
     ...

Of course we would then have to make that clear in our documentation.

r"""
Whether this DM is a positive operator.

Arg:
atol: The tolerance we allow for positivity conditions.
"""
batch_dim = self.ansatz.batch_size
if batch_dim > 1:
Expand All @@ -64,18 +66,20 @@ def is_positive(self) -> bool:
gamma_A = A[:m, m:]

if (
math.real(math.norm(gamma_A - math.conj(gamma_A.T))) > settings.ATOL
math.real(math.norm(gamma_A - math.conj(gamma_A.T))) > atol
): # checks if gamma_A is Hermitian
return False

return all(math.real(math.eigvals(gamma_A)) >= 0)
return all(math.real(math.eigvals(gamma_A)) >= -atol)

@property
def is_physical(self) -> bool:
def is_physical(self, atol: float = settings.ATOL) -> bool:
r"""
Whether this DM is a physical density operator.

Arg:
atol: the tolerance we allow for physicality conditions.
"""
return self.is_positive and math.allclose(self.probability, 1, settings.ATOL)
return self.is_positive(atol) and math.allclose(self.probability, 1, atol)

@property
def probability(self) -> float:
Expand Down
11 changes: 6 additions & 5 deletions mrmustard/lab_dev/states/ket.py
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Expand Up @@ -56,11 +56,14 @@ class Ket(State):

short_name = "Ket"

@property
def is_physical(self) -> bool:
def is_physical(self, atol: float = settings.ATOL) -> bool:
r"""
Whether the ket object is a physical one.

Arg:
atol: The tolerance we allow for physicality conditions. The default value is settings.ATOL.
"""

batch_dim = self.ansatz.batch_size
if batch_dim > 1:
raise ValueError(
Expand All @@ -69,9 +72,7 @@ def is_physical(self) -> bool:

A = self.ansatz.A[0]

return all(math.abs(math.eigvals(A)) < 1) and math.allclose(
self.probability, 1, settings.ATOL
)
return all(math.abs(math.eigvals(A)) < 1) and math.allclose(self.probability, 1, atol)

@property
def probability(self) -> float:
Expand Down
26 changes: 16 additions & 10 deletions mrmustard/lab_dev/transformations/base.py
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Expand Up @@ -356,10 +356,12 @@ class Channel(Map):

short_name = "Ch"

@property
def is_CP(self) -> bool:
def is_CP(self, atol: float = settings.ATOL) -> bool:
r"""
Whether this channel is completely positive (CP).

Arg:
atol: The tolerance we allow for CP conditions (default value is settings.ATOL)
"""
batch_dim = self.ansatz.batch_size
if batch_dim > 1:
Expand All @@ -371,30 +373,34 @@ def is_CP(self) -> bool:
gamma_A = A[0, :m, m:]

if (
math.real(math.norm(gamma_A - math.conj(gamma_A.T))) > settings.ATOL
math.real(math.norm(gamma_A - math.conj(gamma_A.T))) > atol
): # checks if gamma_A is Hermitian
return False

return all(math.real(math.eigvals(gamma_A)) > -settings.ATOL)
return all(math.real(math.eigvals(gamma_A)) > -atol)

@property
def is_TP(self) -> bool:
def is_TP(self, atol: float = settings.ATOL) -> bool:
r"""
Whether this channel is trace preserving (TP).

Arg:
atol: The tolerance we allow for TP condition (default value is settings.ATOL)
"""
A = self.ansatz.A
m = A.shape[-1] // 2
gamma_A = A[0, :m, m:]
lambda_A = A[0, m:, m:]
temp_A = gamma_A + math.conj(lambda_A.T) @ math.inv(math.eye(m) - gamma_A.T) @ lambda_A
return math.real(math.norm(temp_A - math.eye(m))) < settings.ATOL
return math.real(math.norm(temp_A - math.eye(m))) < atol

@property
def is_physical(self) -> bool:
def is_physical(self, atol: float = settings.ATOL) -> bool:
r"""
Whether this channel is physical (i.e. CPTP).

Arg:
atol: The tolerance we allow for CPTP conditions (default value is settings.ATOL)
"""
return self.is_CP and self.is_TP
return self.is_CP(atol) and self.is_TP(atol)

@property
def XY(self) -> tuple[ComplexMatrix, ComplexMatrix]:
Expand Down
10 changes: 5 additions & 5 deletions tests/test_lab_dev/test_states/test_dm.py
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Expand Up @@ -380,18 +380,18 @@ def test_random(self, modes):

@pytest.mark.parametrize("modes", [[9, 2], [0, 1, 2, 3, 4]])
def test_is_positive(self, modes):
assert (Ket.random(modes) >> Attenuator(modes)).is_positive
assert (Ket.random(modes) >> Attenuator(modes)).is_positive()
A = np.zeros([2 * len(modes), 2 * len(modes)])
A[0, -1] = 1.0
rho = DM.from_bargmann(
modes, [A, [complex(0)] * 2 * len(modes), [complex(1)]]
) # this test fails at the hermitian check
assert not rho.is_positive
assert not rho.is_positive()

@pytest.mark.parametrize("modes", [range(10), [0, 1]])
def test_is_physical(self, modes):
rho = DM.random(modes)
assert rho.is_physical
assert rho.is_physical()
rho = 2 * rho
assert not rho.is_physical
assert Ket.random(modes).dm().is_physical
assert not rho.is_physical()
assert Ket.random(modes).dm().is_physical()
2 changes: 1 addition & 1 deletion tests/test_lab_dev/test_states/test_ket.py
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Expand Up @@ -447,4 +447,4 @@ def test_ipython_repr_too_many_dims(self):
assert isinstance(wires, HTML)

def test_is_physical(self):
assert Ket.random([0, 1]).is_physical
assert Ket.random([0, 1]).is_physical()
6 changes: 3 additions & 3 deletions tests/test_lab_dev/test_transformations/test_transformations_base.py
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Expand Up @@ -187,13 +187,13 @@ def test_random(self):
def test_is_CP(self, modes):
u = Unitary.random(modes).ansatz
kraus = u @ u.conj
assert Channel.from_bargmann(modes, modes, kraus.triple).is_CP
assert Channel.from_bargmann(modes, modes, kraus.triple).is_CP()

def test_is_TP(self):
assert Attenuator([0, 1], 0.5).is_CP
assert Attenuator([0, 1], 0.5).is_TP()

def test_is_physical(self):
assert Channel.random(range(5)).is_physical
assert Channel.random(range(5)).is_physical()

def test_XY(self):
U = Unitary.random([0, 1])
Expand Down
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