def average_gate_fidelity(oper, target=None):
"""
Given a Qobj representing the supermatrix form of a map, returns the
average gate fidelity (pseudo-metric) of that map.
Parameters
----------
A : Qobj
Quantum object representing a superoperator.
target : Qobj
Quantum object representing the target unitary; the inverse
is applied before evaluating the fidelity.
Returns
-------
fid : float
Fidelity pseudo-metric between A and the identity superoperator,
or between A and the target superunitary.
"""
kraus_form = to_kraus(oper)
d = kraus_form[0].shape[0]
if kraus_form[0].shape[1] != d:
return TypeError("Average gate fidelity only implemented for square "
"superoperators.")
if target is None:
return (d + np.sum([np.abs(A_k.tr())**2
for A_k in kraus_form])) / (d**2 + d)
else:
return (d + np.sum([np.abs((A_k * target.dag()).tr())**2
for A_k in kraus_form])) / (d**2 + d)
def average_gate_fidelity(oper, target=None):
"""
Given a Qobj representing the supermatrix form of a map, returns the
average gate fidelity (pseudo-metric) of that map.
Parameters
----------
A : Qobj
Quantum object representing a superoperator.
target : Qobj
Quantum object representing the target unitary; the inverse
is applied before evaluating the fidelity.
Returns
-------
fid : float
Fidelity pseudo-metric between A and the identity superoperator,
or between A and the target superunitary.
"""
kraus_form = to_kraus(oper)
d = kraus_form[0].shape[0]
if kraus_form[0].shape[1] != d:
return TypeError("Average gate fidelity only implemented for square "
"superoperators.")
if target is None:
return (d + np.sum([np.abs(A_k.tr())**2
for A_k in kraus_form])) / (d**2 + d)
else:
return (d + np.sum([np.abs((A_k * target.dag()).tr())**2
for A_k in kraus_form])) / (d**2 + d)
def average_gate_fidelity(oper):
"""
Given a Qobj representing the supermatrix form of a map, returns the
average gate fidelity (pseudo-metric) of that map.
Parameters
----------
A : Qobj
Quantum object representing a superoperator.
Returns
-------
fid : float
Fidelity pseudo-metric between A and the identity superoperator.
"""
kraus_form = to_kraus(oper)
d = kraus_form[0].shape[0]
if kraus_form[0].shape[1] != d:
return TypeError("Average gate fielity only implemented for square "
"superoperators.")
return (
d + np.sum([
np.abs(A_k.tr())**2
for A_k in kraus_form
])
) / (d**2 + d)
def test_NeglectSmallKraus(self):
"""
Superoperator: Convert Kraus to Choi matrix and back. Neglect tiny Kraus operators.
"""
zero = asarray([[1], [0]], dtype=complex)
one = asarray([[0], [1]], dtype=complex)
zero_log = kron(kron(zero, zero), zero)
one_log = kron(kron(one, one), one)
# non-square Kraus operator (isometry)
kraus = Qobj(zero_log @ zero.T + one_log @ one.T)
super = sprepost(kraus, kraus.dag())
# 1 non-zero Kraus operator the rest are zero
sixteen_kraus_ops = to_kraus(super, tol=0.0)
# default is tol=1e-9
one_kraus_op = to_kraus(super)
assert_(len(sixteen_kraus_ops) == 16 and len(one_kraus_op) == 1)
assert_((one_kraus_op[0] - kraus).norm() < tol)
def test_NonSquareKrausSuperChoi(self):
"""
Superoperator: Convert non-square Kraus operator to Super + Choi matrix and back.
"""
zero = asarray([[1], [0]], dtype=complex)
one = asarray([[0], [1]], dtype=complex)
zero_log = kron(kron(zero, zero), zero)
one_log = kron(kron(one, one), one)
# non-square Kraus operator (isometry)
kraus = Qobj(zero_log @ zero.T + one_log @ one.T)
super = sprepost(kraus, kraus.dag())
choi = to_choi(super)
op1 = to_kraus(super)
op2 = to_kraus(choi)
op3 = to_super(choi)
assert_(choi.type == "super" and choi.superrep == "choi")
assert_(super.type == "super" and super.superrep == "super")
assert_((op1[0] - kraus).norm() < 1e-8)
assert_((op2[0] - kraus).norm() < 1e-8)
assert_((op3 - super).norm() < 1e-8)
def test_ChoiKrausChoi(self, superoperator):
"""
Superoperator: Convert superoperator to Choi matrix and back.
"""
choi_matrix = to_choi(superoperator)
kraus_ops = to_kraus(choi_matrix)
test_choi = kraus_to_choi(kraus_ops)
# Assert both that the result is close to expected, and has the right
# type.
assert (test_choi - choi_matrix).norm() < tol
assert choi_matrix.type == "super" and choi_matrix.superrep == "choi"
assert test_choi.type == "super" and test_choi.superrep == "choi"
def test_ChoiKrausChoi(self):
"""
Superoperator: Convert superoperator to Choi matrix and back.
"""
superoperator = rand_super()
choi_matrix = to_choi(superoperator)
kraus_ops = to_kraus(choi_matrix)
test_choi = kraus_to_choi(kraus_ops)
# Assert both that the result is close to expected, and has the right
# type.
assert_((test_choi - choi_matrix).norm() < tol)
assert_(choi_matrix.type == "super" and choi_matrix.superrep == "choi")
assert_(test_choi.type == "super" and test_choi.superrep == "choi")
def test_ChoiKrausChoi(self):
"""
Superoperator: Converting superoperator to Choi matrix and back.
"""
superoperator = rand_super()
choi_matrix = to_choi(superoperator)
kraus_ops = to_kraus(choi_matrix)
test_choi = kraus_to_choi(kraus_ops)
# Assert both that the result is close to expected, and has the right
# type.
assert_((test_choi - choi_matrix).norm() < 1e-12)
assert_(choi_matrix.type == "super" and choi_matrix.superrep == "choi")
assert_(test_choi.type == "super" and test_choi.superrep == "choi")
def average_gate_fidelity(oper):
"""
Given a Qobj representing the supermatrix form of a map, returns the
average gate fidelity (pseudo-metric) of that map.
Parameters
----------
A : Qobj
Quantum object representing a superoperator.
Returns
-------
fid : float
Fidelity pseudo-metric between A and the identity superoperator.
"""
kraus_form = to_kraus(oper)
d = kraus_form[0].shape[0]
if kraus_form[0].shape[1] != d:
return TypeError("Average gate fielity only implemented for square "
"superoperators.")
return (d + np.sum([np.abs(A_k.tr())**2
for A_k in kraus_form])) / (d**2 + d)
