partial application of multiqubit gates
This commit is contained in:
Daniel Tsvetkov
parent
7dbbb87c0b
commit
60a11f143e
505
lib.py
505
lib.py
@ -13,6 +13,7 @@ ListOrNdarray = Union[list, np.ndarray]
|
||||
|
||||
REPR_EMPTY_SET = "Ø"
|
||||
REPR_TENSOR_OP = "⊗"
|
||||
REPR_TARGET = "⊕"
|
||||
REPR_GREEK_BETA = "β"
|
||||
REPR_GREEK_PSI = "ψ"
|
||||
REPR_GREEK_PHI = "φ"
|
||||
@ -26,7 +27,8 @@ UNIVERSE_STATES = []
|
||||
|
||||
|
||||
class Matrix(object):
|
||||
"""Wraps a Matrix... it's for my understanding, this could easily probably be np.array"""
|
||||
"""Wraps a Matrix... it's for my understanding, this could easily
|
||||
probably be np.array"""
|
||||
|
||||
def __init__(self, m: ListOrNdarray = None, *args, **kwargs):
|
||||
"""
|
||||
@ -52,8 +54,6 @@ class Matrix(object):
|
||||
def __eq__(self, other):
|
||||
if isinstance(other, Complex):
|
||||
return bool(np.allclose(self.m, other))
|
||||
elif isinstance(other, PartialQubit):
|
||||
return False
|
||||
return np.allclose(self.m, other.m)
|
||||
|
||||
def __mul_or_kron__(self, other):
|
||||
@ -182,7 +182,9 @@ class State(Vector):
|
||||
def to_bloch_angles(self):
|
||||
"""Returns the angles of this state on the Bloch sphere"""
|
||||
if not self.m.shape == (2, 1):
|
||||
raise Exception("State needs to describe only 1 qubit on the bloch sphere (2x1 matrix)")
|
||||
raise Exception(
|
||||
"State needs to describe only 1 qubit on the bloch sphere ("
|
||||
"2x1 matrix)")
|
||||
m0, m1 = self.m[0][0], self.m[1][0]
|
||||
|
||||
# theta is between 0 and pi
|
||||
@ -193,7 +195,8 @@ class State(Vector):
|
||||
|
||||
div = np.sin(theta / 2)
|
||||
if div == 0:
|
||||
# here is doesn't matter what phi is as phase at the poles is arbitrary
|
||||
# here is doesn't matter what phi is as phase at the poles is
|
||||
# arbitrary
|
||||
phi = 0
|
||||
else:
|
||||
exp = m1 / div
|
||||
@ -234,10 +237,13 @@ class State(Vector):
|
||||
return repr(used_state)
|
||||
except:
|
||||
...
|
||||
next_state_sub = ''.join([REPR_MATH_SUBSCRIPT_NUMBERS[int(d)] for d in str(len(UNIVERSE_STATES))])
|
||||
next_state_sub = ''.join(
|
||||
[REPR_MATH_SUBSCRIPT_NUMBERS[int(d)] for d in
|
||||
str(len(UNIVERSE_STATES))])
|
||||
self.name = '{}{}'.format(REPR_GREEK_PSI, next_state_sub)
|
||||
UNIVERSE_STATES.append(self)
|
||||
# matrix_rep = "{}".format(self.m).replace('[', '').replace(']', '').replace('\n', '|').strip()
|
||||
# matrix_rep = "{}".format(self.m).replace('[', '').replace(']',
|
||||
# '').replace('\n', '|').strip()
|
||||
# state_name = '|{}> = {}'.format(self.name, matrix_rep)
|
||||
state_name = '|{}>'.format(self.name)
|
||||
return state_name
|
||||
@ -251,7 +257,8 @@ class State(Vector):
|
||||
return np.sqrt((self.inner(self)).m).item(0)
|
||||
|
||||
def is_orthogonal(self, other):
|
||||
"""If the inner (dot) product is zero, this vector is orthogonal to other"""
|
||||
"""If the inner (dot) product is zero, this vector is orthogonal to
|
||||
other"""
|
||||
return self.inner(other) == 0
|
||||
|
||||
def get_prob_from_measurement_op(self, m_op):
|
||||
@ -284,8 +291,10 @@ class State(Vector):
|
||||
What about if measured twice but in different bases?
|
||||
E.g. measure1 -> computation -> A
|
||||
measure2 -> +/- basis -> B
|
||||
measure3 -> computation -> should it return A again or random weighted?
|
||||
measure4 -> +/- basis -> should it return B again or random weighted?
|
||||
measure3 -> computation -> should it return A again or
|
||||
random weighted?
|
||||
measure4 -> +/- basis -> should it return B again or
|
||||
random weighted?
|
||||
:return: binary representation of the measured qubit (e.g. "011")
|
||||
"""
|
||||
# if self.measurement_result:
|
||||
@ -320,7 +329,8 @@ class State(Vector):
|
||||
weights = list(np.array(weights) / sum(weights))
|
||||
|
||||
format_str = self.get_fmt_of_element()
|
||||
choices = empty_choices + [format_str.format(i) for i in range(len(weights))]
|
||||
choices = empty_choices + [format_str.format(i) for i in
|
||||
range(len(weights))]
|
||||
weights = empty_weights + weights
|
||||
self.measurement_result = random.choices(choices, weights)[0]
|
||||
|
||||
@ -329,7 +339,8 @@ class State(Vector):
|
||||
def measure_with_op(self, mo):
|
||||
"""
|
||||
Measures with a measurement operator mo
|
||||
TODO: Can't define `mo: MeasurementOperator` because in python you can't declare classes before defining them
|
||||
TODO: Can't define `mo: MeasurementOperator` because in python you
|
||||
can't declare classes before defining them
|
||||
"""
|
||||
m = mo.on(self).m / np.sqrt(mo.get_prob(self))
|
||||
return State(m)
|
||||
@ -341,7 +352,10 @@ class State(Vector):
|
||||
"""
|
||||
max_qubits = int(np.log2(len(self)))
|
||||
if not (0 < qubit_n <= max_qubits):
|
||||
raise Exception("Partial measurement of qubit_n must be between 1 and {}".format(max_qubits))
|
||||
raise Exception(
|
||||
"Partial measurement of qubit_n must be between 1 and {"
|
||||
"}".format(
|
||||
max_qubits))
|
||||
format_str = self.get_fmt_of_element()
|
||||
# e.g. for state |000>:
|
||||
# ['000', '001', '010', '011', '100', '101', '110', '111']
|
||||
@ -352,12 +366,15 @@ class State(Vector):
|
||||
# [0, 1, 4, 5]
|
||||
weights, choices = defaultdict(list), defaultdict(list)
|
||||
for result in [1, 0]:
|
||||
indexes_for_p_0 = [i for i, index in enumerate(partial_measurement_of_qbit) if index == result]
|
||||
indexes_for_p_0 = [i for i, index in
|
||||
enumerate(partial_measurement_of_qbit) if
|
||||
index == result]
|
||||
weights[result] = [self.get_prob(j) for j in indexes_for_p_0]
|
||||
choices[result] = [format_str.format(i) for i in indexes_for_p_0]
|
||||
weights_01 = [sum(weights[0]), sum(weights[1])]
|
||||
measurement_result = random.choices([0, 1], weights_01)[0]
|
||||
normalization_factor = np.sqrt(sum([np.abs(i) ** 2 for i in weights[measurement_result]]))
|
||||
normalization_factor = np.sqrt(
|
||||
sum([np.abs(i) ** 2 for i in weights[measurement_result]]))
|
||||
new_m = weights[measurement_result] / normalization_factor
|
||||
return str(measurement_result), State(new_m.reshape((len(new_m), 1)))
|
||||
|
||||
@ -375,7 +392,9 @@ class State(Vector):
|
||||
bin_length = 2 ** len(bin_repr)
|
||||
arr = [[1] if i == dec_bin else [0] for i in range(bin_length)]
|
||||
except:
|
||||
raise Exception("State from string should be of the form |00..01> with all numbers either 0 or 1")
|
||||
raise Exception(
|
||||
"State from string should be of the form |00..01> with all "
|
||||
"numbers either 0 or 1")
|
||||
return cls(arr)
|
||||
|
||||
@staticmethod
|
||||
@ -405,7 +424,8 @@ def test_measure_partial():
|
||||
|
||||
|
||||
def normalize_state(vector: Vector):
|
||||
"""Normalize a state by dividing by the square root of sum of the squares of states"""
|
||||
"""Normalize a state by dividing by the square root of sum of the squares
|
||||
of states"""
|
||||
norm_coef = np.sqrt(np.sum(np.array(vector.m) ** 2))
|
||||
if norm_coef == 0:
|
||||
raise TypeError("zero-sum vector")
|
||||
@ -464,11 +484,11 @@ class Operator(object):
|
||||
"""An Operator turns one function into another"""
|
||||
self.func = func
|
||||
|
||||
def on(self, *args):
|
||||
return self(*args)
|
||||
def on(self, *args, **kwargs):
|
||||
return self(*args, **kwargs)
|
||||
|
||||
def __call__(self, *args):
|
||||
return self.func(*args)
|
||||
def __call__(self, *args, **kwargs):
|
||||
return self.func(*args, **kwargs)
|
||||
|
||||
|
||||
class LinearOperator(Operator):
|
||||
@ -480,8 +500,10 @@ class LinearOperator(Operator):
|
||||
|
||||
def _is_linear(self):
|
||||
# A function is (jointly) linear in a given set of variables
|
||||
# if all second-order derivatives are identically zero (including mixed ones).
|
||||
# https://stackoverflow.com/questions/36283548/check-if-an-equation-is-linear-for-a-specific-set-of-variables
|
||||
# if all second-order derivatives are identically zero (including
|
||||
# mixed ones).
|
||||
# https://stackoverflow.com/questions/36283548/check-if-an-equation
|
||||
# -is-linear-for-a-specific-set-of-variables
|
||||
expr, vars_ = self.func.expr, self.func.variables
|
||||
for x in vars_:
|
||||
for y in vars_:
|
||||
@ -501,7 +523,8 @@ def test_linear_operator():
|
||||
assert _times_2.on(5) == 10
|
||||
assert _times_2(5) == 10
|
||||
|
||||
assert_raises(TypeError, "Not a linear operator", LinearOperator, sp.Lambda(_x, _x ** 2))
|
||||
assert_raises(TypeError, "Not a linear operator", LinearOperator,
|
||||
sp.Lambda(_x, _x ** 2))
|
||||
|
||||
|
||||
class SquareMatrix(Matrix):
|
||||
@ -515,9 +538,12 @@ class SquareMatrix(Matrix):
|
||||
|
||||
|
||||
class LinearTransformation(LinearOperator, Matrix):
|
||||
def __init__(self, m: ListOrNdarray, func=None, name: str = '', *args, **kwargs):
|
||||
"""LinearTransformation (or linear map) inherits from both LinearOperator and a Matrix
|
||||
It is used to act on a State vector by defining the operator to be the dot product"""
|
||||
def __init__(self, m: ListOrNdarray, func=None, name: str = '', *args,
|
||||
**kwargs):
|
||||
"""LinearTransformation (or linear map) inherits from both
|
||||
LinearOperator and a Matrix
|
||||
It is used to act on a State vector by defining the operator to be
|
||||
the dot product"""
|
||||
self.name = name
|
||||
Matrix.__init__(self, m=m, *args, **kwargs)
|
||||
self.func = func or self.operator_func
|
||||
@ -525,7 +551,8 @@ class LinearTransformation(LinearOperator, Matrix):
|
||||
|
||||
def _is_linear(self):
|
||||
# Every matrix transformation is a linear transformation
|
||||
# https://www.mathbootcamps.com/proof-every-matrix-transformation-is-a-linear-transformation/
|
||||
# https://www.mathbootcamps.com/proof-every-matrix-transformation-is
|
||||
# -a-linear-transformation/
|
||||
return True
|
||||
|
||||
def operator_func(self, other):
|
||||
@ -555,7 +582,8 @@ class UnitaryMatrix(SquareMatrix):
|
||||
raise TypeError("Not a Unitary matrix")
|
||||
|
||||
def _is_unitary(self):
|
||||
"""Checks if the matrix product of itself with conjugate transpose is Identity UU+ = I"""
|
||||
"""Checks if the matrix product of itself with conjugate transpose is
|
||||
Identity UU+ = I"""
|
||||
UU_ = np.dot(self._conjugate_transpose(), self.m)
|
||||
I = np.eye(self.m.shape[0])
|
||||
return np.isclose(UU_, I).all()
|
||||
@ -574,25 +602,67 @@ class HermitianMatrix(SquareMatrix):
|
||||
|
||||
|
||||
class UnitaryOperator(LinearTransformation, UnitaryMatrix):
|
||||
def __init__(self, m: ListOrNdarray, name: str = '', *args, **kwargs):
|
||||
"""UnitaryOperator inherits from both LinearTransformation and a Unitary matrix
|
||||
It is used to act on a State vector by defining the operator to be the dot product"""
|
||||
def __init__(self, m: ListOrNdarray, name: str = '', partials=None, *args,
|
||||
**kwargs):
|
||||
"""UnitaryOperator inherits from both LinearTransformation and a
|
||||
Unitary matrix
|
||||
It is used to act on a State vector by defining the operator to be
|
||||
the dot product
|
||||
|
||||
Partials - a list of partial operators that are used in a multi-qubit
|
||||
UnitaryOperator to define the operator on each qubit. Each element of
|
||||
the list is the Nth partial that is used, i.e. for the first - |0><0|,
|
||||
for the second - |1><1|
|
||||
"""
|
||||
if np.shape(m) != (2, 2) and partials is None:
|
||||
raise Exception("Please define partials in a non-single operator")
|
||||
UnitaryMatrix.__init__(self, m=m, *args, **kwargs)
|
||||
LinearTransformation.__init__(self, m=m, func=self.operator_func, *args, **kwargs)
|
||||
LinearTransformation.__init__(self, m=m, func=self.operator_func, *args,
|
||||
**kwargs)
|
||||
self.name = name
|
||||
self.partials = partials
|
||||
|
||||
def operator_func(self, other, which_qbit=None):
|
||||
this_cols, other_rows = np.shape(self.m)[1], np.shape(other.m)[0]
|
||||
if this_cols != other_rows:
|
||||
if which_qbit is None:
|
||||
raise Exception("Operating dim-{} operator on a dim-{} state. "
|
||||
"Please specify which_qubit to operate on".format(
|
||||
this_cols, other_rows))
|
||||
if this_cols == other_rows:
|
||||
return State(np.dot(self.m, other.m))
|
||||
if which_qbit is None:
|
||||
raise Exception("Operating dim-{} operator on a dim-{} state. "
|
||||
"Please specify which_qubit to operate on".format(
|
||||
this_cols, other_rows))
|
||||
total_qbits = int(np.log2(other_rows))
|
||||
if type(which_qbit) is int:
|
||||
# single qubit-gate
|
||||
assert this_cols == 2
|
||||
assert 0 <= which_qbit < total_qbits
|
||||
extended_m = [self if i == which_qbit else I for i in
|
||||
range(total_qbits)]
|
||||
new_m = np.prod(extended_m).m
|
||||
elif type(which_qbit) is list:
|
||||
# single or multiple qubit-gate
|
||||
assert 1 <= len(which_qbit) < total_qbits
|
||||
assert len(which_qbit) == len(self.partials)
|
||||
assert all([q < total_qbits for q in which_qbit])
|
||||
extended_m, next_partial = [[], []], 0
|
||||
for qbit in range(total_qbits):
|
||||
if qbit not in which_qbit:
|
||||
extended_m[0].append(I)
|
||||
extended_m[1].append(I)
|
||||
else:
|
||||
this_partial = self.partials[next_partial]
|
||||
if this_partial == C_partial:
|
||||
extended_m[0].append(s("|0><0|"))
|
||||
extended_m[1].append(s("|1><1|"))
|
||||
else:
|
||||
extended_m[0].append(I)
|
||||
extended_m[1].append(this_partial)
|
||||
next_partial += 1
|
||||
new_m = sum([np.prod(e).m for e in extended_m])
|
||||
else:
|
||||
raise Exception("which_qubit needs to be either an int of N-th qubit or list")
|
||||
|
||||
extended_m = [self if i == which_qbit else I for i in range(int(np.log2(other_rows)))]
|
||||
extended_op = UnitaryOperator(np.prod(extended_m).m)
|
||||
return State(np.dot(extended_op.m, other.m))
|
||||
return State(np.dot(self.m, other.m))
|
||||
extended_op = UnitaryOperator(new_m, name=self.name, partials=self.partials)
|
||||
return State(np.dot(extended_op.m, other.m))
|
||||
|
||||
def __repr__(self):
|
||||
if self.name:
|
||||
@ -608,14 +678,17 @@ class Gate(UnitaryOperator):
|
||||
|
||||
class HermitianOperator(LinearTransformation, HermitianMatrix):
|
||||
def __init__(self, m: ListOrNdarray, name: str = '', *args, **kwargs):
|
||||
"""HermitianOperator inherits from both LinearTransformation and a Hermitian matrix
|
||||
It is used to act on a State vector by defining the operator to be the dot product"""
|
||||
"""HermitianOperator inherits from both LinearTransformation and a
|
||||
Hermitian matrix
|
||||
It is used to act on a State vector by defining the operator to be
|
||||
the dot product"""
|
||||
self.name = name
|
||||
HermitianMatrix.__init__(self, m=m, *args, **kwargs)
|
||||
LinearOperator.__init__(self, func=self.operator_func, *args, **kwargs)
|
||||
|
||||
def operator_func(self, other):
|
||||
"""This might not return a normalized state vector so don't wrap it in State"""
|
||||
"""This might not return a normalized state vector so don't wrap it
|
||||
in State"""
|
||||
return Vector(np.dot(self.m, other.m))
|
||||
|
||||
def __repr__(self):
|
||||
@ -643,71 +716,6 @@ class DensityMatrix(HermitianOperator):
|
||||
return np.isclose(np.trace(self.m), 1.0)
|
||||
|
||||
|
||||
# How to add a CNOT gate to the Quantum Processor?
|
||||
# Imagine if I have to act on a 3-qubit computer and CNOT(q1, q3)
|
||||
#
|
||||
# Decomposed CNOT :
|
||||
# reverse engineered from
|
||||
# https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the-cnot-matrix-for-a-3-qbit-system-where-the-control-target-qbi
|
||||
#
|
||||
# CNOT(q1, I, q2):
|
||||
# |0><0| x I_2 x I_2 + |1><1| x I_2 x X
|
||||
# np.kron(np.kron(np.outer(_0.m, _0.m), np.eye(2)), np.eye(2)) + np.kron(np.kron(np.outer(_1.m, _1.m), np.eye(2)), X.m)
|
||||
#
|
||||
#
|
||||
# CNOT(q1, q2):
|
||||
# |0><0| x I + |1><1| x X
|
||||
# np.kron(np.outer(_0.m, _0.m), np.eye(2)) + np.kron(np.outer(_1.m, _1.m), X.m)
|
||||
# _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
|
||||
|
||||
class PartialQubit(object):
|
||||
def __init__(self, rpr):
|
||||
self.rpr = rpr
|
||||
self.operator = None
|
||||
|
||||
def __repr__(self):
|
||||
return str("-{}-".format(self.rpr))
|
||||
|
||||
|
||||
C_partial = PartialQubit("C")
|
||||
x_partial = PartialQubit("x")
|
||||
|
||||
|
||||
class TwoQubitOperator(UnitaryOperator):
|
||||
def __init__(self, m: ListOrNdarray, A: PartialQubit, B: PartialQubit,
|
||||
A_p: UnitaryOperator, B_p: UnitaryOperator, *args, **kwargs):
|
||||
super().__init__(m, *args, **kwargs)
|
||||
A.operator, B.operator = self, self
|
||||
self.A = A
|
||||
self.B = B
|
||||
self.A_p = A_p
|
||||
self.B_p = B_p
|
||||
|
||||
A.operator = self
|
||||
B.operator = self
|
||||
|
||||
def verify_step(self, step):
|
||||
if not (step.count(self.A) == 1 and step.count(self.B) == 1):
|
||||
raise RuntimeError("Both {} and {} need to be defined in the same step exactly once".format(
|
||||
self.A, self.B
|
||||
))
|
||||
|
||||
def compose(self, step, state):
|
||||
# _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
|
||||
outer_0, outer_1 = [], []
|
||||
for s in step:
|
||||
if s == self.A:
|
||||
outer_0.append(_0.x(_0))
|
||||
outer_1.append(_1.x(_1))
|
||||
elif s == self.B:
|
||||
outer_0.append(Matrix(self.A_p.m))
|
||||
outer_1.append(Matrix(self.B_p.m))
|
||||
else:
|
||||
outer_0.append(Matrix(s.m))
|
||||
outer_1.append(Matrix(s.m))
|
||||
return reduce((lambda x, y: x * y), outer_0) + reduce((lambda x, y: x * y), outer_1)
|
||||
|
||||
|
||||
"""
|
||||
Define States and Operators
|
||||
"""
|
||||
@ -767,73 +775,92 @@ bell_basis = [b_phi_p, b_psi_p, b_phi_m, b_psi_m]
|
||||
well_known_states = [_p, _m, b_phi_p, b_psi_p, b_phi_m, b_psi_m]
|
||||
|
||||
_ = I = Gate([[1, 0],
|
||||
[0, 1]],
|
||||
name="-")
|
||||
[0, 1]],
|
||||
name="-")
|
||||
|
||||
X = Gate([[0, 1],
|
||||
[1, 0]],
|
||||
name="X")
|
||||
[1, 0]],
|
||||
name="X")
|
||||
|
||||
Y = Gate([[0, -1j],
|
||||
[1j, 0]],
|
||||
name="Y")
|
||||
[1j, 0]],
|
||||
name="Y")
|
||||
|
||||
Z = Gate([[1, 0],
|
||||
[0, -1]],
|
||||
name="Z")
|
||||
|
||||
[0, -1]],
|
||||
name="Z")
|
||||
|
||||
# These are rotations that are specified commonly e.g. in
|
||||
# https://www.quantum-inspire.com/kbase/rotation-operators/
|
||||
# http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere-rotations.pdf
|
||||
# http://www.vcpc.univie.ac.at/~ian/hotlist/qc/talks/bloch-sphere
|
||||
# -rotations.pdf
|
||||
# and elsewhere DO NOT equate X, Y and Z for theta=np.pi
|
||||
# However - they are correct up to a global phase which is all that matters for measurement purposes
|
||||
# However - they are correct up to a global phase which is all that matters
|
||||
# for measurement purposes
|
||||
#
|
||||
|
||||
H = Gate([[1 / np.sqrt(2), 1 / np.sqrt(2)],
|
||||
[1 / np.sqrt(2), -1 / np.sqrt(2)], ],
|
||||
[1 / np.sqrt(2), -1 / np.sqrt(2)], ],
|
||||
name="H")
|
||||
|
||||
# Rotation operators
|
||||
# https://www.quantum-inspire.com/kbase/rx-gate/
|
||||
Rx = lambda theta: Gate([[np.cos(theta / 2), -1j * np.sin(theta / 2)],
|
||||
[-1j * np.sin(theta / 2), np.cos(theta / 2)]],
|
||||
name="Rx")
|
||||
|
||||
[-1j * np.sin(theta / 2), np.cos(theta / 2)]],
|
||||
name="Rx")
|
||||
|
||||
Ry = lambda theta: Gate([[np.cos(theta / 2), -np.sin(theta / 2)],
|
||||
[np.sin(theta / 2), np.cos(theta / 2)]],
|
||||
name="Ry")
|
||||
|
||||
[np.sin(theta / 2), np.cos(theta / 2)]],
|
||||
name="Ry")
|
||||
|
||||
Rz = lambda theta: Gate([[np.power(np.e, -1j * theta / 2), 0],
|
||||
[0, np.power(np.e, 1j * theta / 2)]],
|
||||
name="Rz")
|
||||
|
||||
[0, np.power(np.e, 1j * theta / 2)]],
|
||||
name="Rz")
|
||||
|
||||
# See [T-Gate](https://www.quantum-inspire.com/kbase/t-gate/)
|
||||
T = lambda phi: Gate([[1, 0],
|
||||
[0, np.power(np.e, 1j * phi / 2)]],
|
||||
[0, np.power(np.e, 1j * phi / 2)]],
|
||||
name="T")
|
||||
|
||||
CNOT = TwoQubitOperator([
|
||||
# How to add a CNOT gate to the Quantum Processor?
|
||||
# Imagine if I have to act on a 3-qubit computer and CNOT(q1, q3)
|
||||
#
|
||||
# Decomposed CNOT :
|
||||
# reverse engineered from
|
||||
# https://quantumcomputing.stackexchange.com/questions/4252/how-to-derive-the
|
||||
# -cnot-matrix-for-a-3-qbit-system-where-the-control-target-qbi
|
||||
#
|
||||
# CNOT(q1, I, q2):
|
||||
# |0><0| x I_2 x I_2 + |1><1| x I_2 x X
|
||||
# np.kron(np.kron(np.outer(_0.m, _0.m), np.eye(2)), np.eye(2)) + np.kron(
|
||||
# np.kron(np.outer(_1.m, _1.m), np.eye(2)), X.m)
|
||||
#
|
||||
#
|
||||
# CNOT(q1, q2):
|
||||
# |0><0| x I + |1><1| x X
|
||||
# np.kron(np.outer(_0.m, _0.m), np.eye(2)) + np.kron(np.outer(_1.m, _1.m), X.m)
|
||||
# _0.x(_0) * Matrix(I.m) + _1.x(_1) * Matrix(X.m)
|
||||
|
||||
C_partial = Gate(I.m, name="C")
|
||||
x_partial = Gate(X.m, name=REPR_TARGET)
|
||||
|
||||
CNOT = Gate([
|
||||
[1, 0, 0, 0],
|
||||
[0, 1, 0, 0],
|
||||
[0, 0, 0, 1],
|
||||
[0, 0, 1, 0],
|
||||
], C_partial, x_partial, I, X)
|
||||
], name="CNOT", partials=[C_partial, x_partial])
|
||||
|
||||
|
||||
# TOFFOLLI_GATE = ThreeQubitOperator([
|
||||
# [1, 0, 0, 0, 0, 0, 0, 0],
|
||||
# [0, 1, 0, 0, 0, 0, 0, 0],
|
||||
# [0, 0, 1, 0, 0, 0, 0, 0],
|
||||
# [0, 0, 0, 1, 0, 0, 0, 0],
|
||||
# [0, 0, 0, 0, 1, 0, 0, 0],
|
||||
# [0, 0, 0, 0, 0, 1, 0, 0],
|
||||
# [0, 0, 0, 0, 0, 0, 0, 1],
|
||||
# [0, 0, 0, 0, 0, 0, 1, 0],
|
||||
# ], C_partial, C_partial, x_partial, I, I, X)
|
||||
TOFF = Gate([
|
||||
[1, 0, 0, 0, 0, 0, 0, 0],
|
||||
[0, 1, 0, 0, 0, 0, 0, 0],
|
||||
[0, 0, 1, 0, 0, 0, 0, 0],
|
||||
[0, 0, 0, 1, 0, 0, 0, 0],
|
||||
[0, 0, 0, 0, 1, 0, 0, 0],
|
||||
[0, 0, 0, 0, 0, 1, 0, 0],
|
||||
[0, 0, 0, 0, 0, 0, 0, 1],
|
||||
[0, 0, 0, 0, 0, 0, 1, 0],
|
||||
], partials=[C_partial, C_partial, x_partial])
|
||||
|
||||
|
||||
def assert_raises(exception, msg, callable, *args, **kwargs):
|
||||
@ -857,12 +884,15 @@ def test_unitary_hermitian():
|
||||
# Unitary is UU+ = I; Hermitian is U = U+
|
||||
# Matrixes could be either, neither or both
|
||||
# Quantum operators (gates) are described *only* by unitary transformations
|
||||
# Hermitian operators are used for measurement operators - https://towardsdatascience.com/understanding-basics-of-measurements-in-quantum-computation-4c885879eba0
|
||||
# Hermitian operators are used for measurement operators -
|
||||
# https://towardsdatascience.com/understanding-basics-of-measurements-in
|
||||
# -quantum-computation-4c885879eba0
|
||||
h_not_u = [
|
||||
[1, 0],
|
||||
[0, 2],
|
||||
]
|
||||
assert_not_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix, h_not_u)
|
||||
assert_not_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix,
|
||||
h_not_u)
|
||||
assert_raises(TypeError, "Not a Unitary matrix", UnitaryMatrix, h_not_u)
|
||||
|
||||
u_not_h = [
|
||||
@ -876,14 +906,16 @@ def test_unitary_hermitian():
|
||||
[0, 1],
|
||||
[1, 0],
|
||||
]
|
||||
assert_not_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix, u_and_h)
|
||||
assert_not_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix,
|
||||
u_and_h)
|
||||
assert_not_raises(TypeError, "Not a Unitary matrix", UnitaryMatrix, u_and_h)
|
||||
|
||||
not_u_not_h = [
|
||||
[1, 2],
|
||||
[0, 1],
|
||||
]
|
||||
assert_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix, not_u_not_h)
|
||||
assert_raises(TypeError, "Not a Hermitian matrix", HermitianMatrix,
|
||||
not_u_not_h)
|
||||
assert_raises(TypeError, "Not a Unitary matrix", UnitaryMatrix, not_u_not_h)
|
||||
|
||||
|
||||
@ -947,32 +979,69 @@ def test_eigenstuff():
|
||||
[(1.0, HorizontalVector([1., 0.])), (0., HorizontalVector([0., 1.]))]
|
||||
|
||||
|
||||
def test_partials():
|
||||
# normal 2 qbit state
|
||||
assert CNOT.on(s("|00>")) == s("|00>")
|
||||
assert CNOT.on(s("|10>")) == s("|11>")
|
||||
assert_raises(Exception,
|
||||
"Operating dim-4 operator on a dim-8 state. Please specify "
|
||||
"which_qubit to operate on",
|
||||
CNOT.on, s("|100>"))
|
||||
# apply on 0, 1 of 3qbit state
|
||||
assert CNOT.on(s("|000>"), which_qbit=[0, 1]) == s("|000>")
|
||||
assert CNOT.on(s("|100>"), which_qbit=[0, 1]) == s("|110>")
|
||||
# apply on 1, 2 of 3qbit state
|
||||
assert CNOT.on(s("|000>"), which_qbit=[1, 2]) == s("|000>")
|
||||
assert CNOT.on(s("|010>"), which_qbit=[1, 2]) == s("|011>")
|
||||
# apply on 0, 2 of 3qbit state
|
||||
assert CNOT.on(s("|000>"), which_qbit=[0, 2]) == s("|000>")
|
||||
assert CNOT.on(s("|100>"), which_qbit=[0, 2]) == s("|101>")
|
||||
# apply on 0, 2 of 4qbit state
|
||||
assert CNOT.on(s("|1000>"), which_qbit=[0, 2]) == s("|1010>")
|
||||
# apply on 0, 3 of 4qbit state
|
||||
assert CNOT.on(s("|1000>"), which_qbit=[0, 3]) == s("|1001>")
|
||||
|
||||
# test Toffoli gate
|
||||
# assert TOFF.on(s("|000>")) == s("|000>")
|
||||
# assert TOFF.on(s("|100>")) == s("|100>")
|
||||
# assert TOFF.on(s("|110>")) == s("|111>")
|
||||
# assert TOFF.on(s("|1100>"), which_qbit=[0, 1, 3]) == s("|1101>")
|
||||
|
||||
|
||||
def test():
|
||||
# Test properties of Hilbert vector space
|
||||
# The four postulates of Quantum Mechanics
|
||||
# I: States | Associated to any physical system is a complex vector space
|
||||
# known as the state space of the system. If the system is closed
|
||||
# known as the state space of the system. If the system is
|
||||
# closed
|
||||
# then the system is described completely by its state vector
|
||||
# which is a unit vector in the space.
|
||||
# Mathematically, this vector space is also a function space
|
||||
assert _0 + _1 == _1 + _0 # commutativity of vector addition
|
||||
assert _0 + (_1 + _p) == (_0 + _1) + _p # associativity of vector addition
|
||||
assert 8 * (_0 + _1) == 8 * _0 + 8 * _1 # Linear when multiplying by constants
|
||||
assert 8 * (
|
||||
_0 + _1) == 8 * _0 + 8 * _1 # Linear when multiplying by
|
||||
# constants
|
||||
assert _0.inner(_0) == 1 # parallel have 1 product
|
||||
assert _0.inner(_1) == 0 # orthogonal have 0 product
|
||||
assert _0.is_orthogonal(_1)
|
||||
assert _1.inner(8 * _0) == 8 * _1.inner(_0) # Inner product is linear multiplied by constants
|
||||
assert _p.inner(_1 + _0) == _p.inner(_1) + _p.inner(_0) # Inner product is linear in superpos of vectors
|
||||
assert _1.inner(8 * _0) == 8 * _1.inner(
|
||||
_0) # Inner product is linear multiplied by constants
|
||||
assert _p.inner(_1 + _0) == _p.inner(_1) + _p.inner(
|
||||
_0) # Inner product is linear in superpos of vectors
|
||||
|
||||
assert np.isclose(_1.length(), 1.0) # all of the vector lengths are normalized
|
||||
assert np.isclose(_1.length(),
|
||||
1.0) # all of the vector lengths are normalized
|
||||
assert np.isclose(_0.length(), 1.0)
|
||||
assert np.isclose(_p.length(), 1.0)
|
||||
|
||||
assert _0.inner(_1) == _1.inner(_0).complex_conjugate() # non-commutative inner product
|
||||
assert _0.inner(_1) == _1.inner(
|
||||
_0).complex_conjugate() # non-commutative inner product
|
||||
|
||||
test_to_from_angles()
|
||||
|
||||
# II: Dynamics | The evolution of a closed system is described by a unitary transformation
|
||||
# II: Dynamics | The evolution of a closed system is described by a
|
||||
# unitary transformation
|
||||
#
|
||||
test_linear_operator()
|
||||
|
||||
@ -994,14 +1063,23 @@ def test():
|
||||
# Test Pauli rotation gates
|
||||
testRotPauli()
|
||||
|
||||
# III: Measurement | A quantum measurement is described by an orthonormal basis |e_j>
|
||||
# for state space. If the initial state of the system is |ψ>
|
||||
# then we get outcome j with probability pr(j) = |<e_j|ψ>|^2
|
||||
# Test 2+ qbit gates and partials
|
||||
test_partials()
|
||||
|
||||
# III: Measurement | A quantum measurement is described by an orthonormal
|
||||
# basis |e_j>
|
||||
# for state space. If the initial state of the system
|
||||
# is |ψ>
|
||||
# then we get outcome j with probability pr(j) =
|
||||
# |<e_j|ψ>|^2
|
||||
# Note: The postulates are applicable on closed, isolated systems.
|
||||
# Systems that are closed and are described by unitary time evolution by a Hamiltonian
|
||||
# can be measured by projective measurements. Systems are not closed in reality and hence
|
||||
# Systems that are closed and are described by unitary time
|
||||
# evolution by a Hamiltonian
|
||||
# can be measured by projective measurements. Systems are not
|
||||
# closed in reality and hence
|
||||
# are immeasurable using projective measurements.
|
||||
# POVM (Positive Operator-Valued Measure) is a restriction on the projective measurements,
|
||||
# POVM (Positive Operator-Valued Measure) is a restriction on the
|
||||
# projective measurements,
|
||||
# such that it encompasses everything except the environment.
|
||||
|
||||
assert _0.get_prob(0) == 1 # Probability for |0> in 0 is 1
|
||||
@ -1052,7 +1130,8 @@ def test():
|
||||
assert CNOT.on(_1 * _0) == _1 * _1
|
||||
assert CNOT.on(_1 * _1) == _1 * _0
|
||||
|
||||
# ALL FOUR NOW - Create a Bell state (I) that has H|0> (II), measures (III) and composition in CNOT (IV)
|
||||
# ALL FOUR NOW - Create a Bell state (I) that has H|0> (II), measures (
|
||||
# III) and composition in CNOT (IV)
|
||||
# Bell state
|
||||
# First - create a superposition
|
||||
superpos = H.on(_0)
|
||||
@ -1065,10 +1144,14 @@ def test():
|
||||
[0.],
|
||||
[1 / np.sqrt(2)], ])
|
||||
|
||||
assert np.isclose(bell.get_prob(0b00), 0.5) # Probability for bell in 00 is 0.5
|
||||
assert np.isclose(bell.get_prob(0b01), 0) # Probability for bell in 01 is 0.
|
||||
assert np.isclose(bell.get_prob(0b10), 0) # Probability for bell in 10 is 0.
|
||||
assert np.isclose(bell.get_prob(0b11), 0.5) # Probability for bell in 11 is 0.5
|
||||
assert np.isclose(bell.get_prob(0b00),
|
||||
0.5) # Probability for bell in 00 is 0.5
|
||||
assert np.isclose(bell.get_prob(0b01),
|
||||
0) # Probability for bell in 01 is 0.
|
||||
assert np.isclose(bell.get_prob(0b10),
|
||||
0) # Probability for bell in 10 is 0.
|
||||
assert np.isclose(bell.get_prob(0b11),
|
||||
0.5) # Probability for bell in 11 is 0.5
|
||||
|
||||
################################
|
||||
assert _0.x(_0) == Matrix([[1, 0],
|
||||
@ -1108,16 +1191,17 @@ def naive_load_test(N):
|
||||
from time import time
|
||||
from sys import getsizeof
|
||||
|
||||
print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
|
||||
"qbits",
|
||||
"kron_len",
|
||||
"mem_used",
|
||||
"mem_per_q",
|
||||
"getsizeof",
|
||||
"getsiz/len",
|
||||
"nbytes",
|
||||
"nbytes/len",
|
||||
"time"))
|
||||
print(
|
||||
"{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
|
||||
"qbits",
|
||||
"kron_len",
|
||||
"mem_used",
|
||||
"mem_per_q",
|
||||
"getsizeof",
|
||||
"getsiz/len",
|
||||
"nbytes",
|
||||
"nbytes/len",
|
||||
"time"))
|
||||
|
||||
_0 = State([[1], [0]], name='0')
|
||||
|
||||
@ -1131,16 +1215,18 @@ def naive_load_test(N):
|
||||
len_m = len(m)
|
||||
elapsed = time() - start
|
||||
mem_b = process.memory_info().rss - mem_init
|
||||
print("{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10}".format(
|
||||
i,
|
||||
len(m),
|
||||
sizeof_fmt(mem_b),
|
||||
sizeof_fmt(mem_b / len_m),
|
||||
sizeof_fmt(getsizeof(m)),
|
||||
sizeof_fmt(getsizeof(m) / len_m),
|
||||
sizeof_fmt(m.m.nbytes),
|
||||
sizeof_fmt(m.m.nbytes / len_m),
|
||||
np.round(elapsed, 2)))
|
||||
print(
|
||||
"{:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {:>10} {"
|
||||
":>10}".format(
|
||||
i,
|
||||
len(m),
|
||||
sizeof_fmt(mem_b),
|
||||
sizeof_fmt(mem_b / len_m),
|
||||
sizeof_fmt(getsizeof(m)),
|
||||
sizeof_fmt(getsizeof(m) / len_m),
|
||||
sizeof_fmt(m.m.nbytes),
|
||||
sizeof_fmt(m.m.nbytes / len_m),
|
||||
np.round(elapsed, 2)))
|
||||
|
||||
gc.collect()
|
||||
|
||||
@ -1160,12 +1246,15 @@ class QuantumCircuit(object):
|
||||
|
||||
def add_row_step(self, row: int, step: int, qbit_state):
|
||||
if len(self.steps) <= step:
|
||||
self.steps += [[I for _ in range(self.n_qubits)] for _ in range(len(self.steps) - step + 1)]
|
||||
self.steps += [[I for _ in range(self.n_qubits)] for _ in
|
||||
range(len(self.steps) - step + 1)]
|
||||
self.steps[step][row] = qbit_state
|
||||
|
||||
def add_step(self, step_data: list):
|
||||
if len(step_data) != self.n_qubits:
|
||||
raise RuntimeError("Length of step is: {}, should be: {}".format(len(step_data), self.n_qubits))
|
||||
raise RuntimeError(
|
||||
"Length of step is: {}, should be: {}".format(len(step_data),
|
||||
self.n_qubits))
|
||||
step_i = len(step_data)
|
||||
for row, qubit_state in enumerate(step_data):
|
||||
self.add_row_step(row, step_i, qubit_state)
|
||||
@ -1187,7 +1276,8 @@ class QuantumCircuit(object):
|
||||
|
||||
def compose_quantum_state(self, step):
|
||||
partials = [op for op in step if isinstance(op, PartialQubit)]
|
||||
# TODO: No more than 1 TwoQubitGate **OR** UnitaryOperator can be used in a step
|
||||
# TODO: No more than 1 TwoQubitGate **OR** UnitaryOperator can be
|
||||
# used in a step
|
||||
for partial in partials:
|
||||
two_qubit_op = partial.operator
|
||||
two_qubit_op.verify_step()
|
||||
@ -1205,7 +1295,8 @@ class QuantumCircuit(object):
|
||||
if not self.current_quantum_state:
|
||||
self.current_quantum_state = step_quantum_state
|
||||
else:
|
||||
self.current_quantum_state = step_quantum_state.inner(self.current_quantum_state)
|
||||
self.current_quantum_state = step_quantum_state.inner(
|
||||
self.current_quantum_state)
|
||||
self.current_step += 1
|
||||
|
||||
def run(self):
|
||||
@ -1235,9 +1326,11 @@ class QuantumProcessor(object):
|
||||
|
||||
def __init__(self, circuit: QuantumCircuit):
|
||||
if circuit.rows != circuit.n_qubits:
|
||||
raise Exception("Declared circuit with n_qubits: {} but called add_row: {}".format(
|
||||
circuit.n_qubits, circuit.rows
|
||||
))
|
||||
raise Exception(
|
||||
"Declared circuit with n_qubits: {} but called add_row: {"
|
||||
"}".format(
|
||||
circuit.n_qubits, circuit.rows
|
||||
))
|
||||
self.circuit = circuit
|
||||
self.c_step = 0
|
||||
self.c_q_state = None
|
||||
@ -1245,13 +1338,6 @@ class QuantumProcessor(object):
|
||||
self.reset()
|
||||
|
||||
def compose_quantum_state(self, step):
|
||||
if any([type(s) is PartialQubit for s in step]):
|
||||
two_qubit_gates = filter(lambda s: type(s) is PartialQubit, step)
|
||||
state = []
|
||||
for two_qubit_gate in two_qubit_gates:
|
||||
two_qubit_gate.operator.verify_step(step)
|
||||
state = two_qubit_gate.operator.compose(step, state)
|
||||
return state
|
||||
return reduce((lambda x, y: x * y), step)
|
||||
|
||||
def step(self):
|
||||
@ -1327,7 +1413,8 @@ def test_light():
|
||||
ver_filter = MeasurementOperator.create_from_basis(Matrix(_1.m), name='v')
|
||||
|
||||
def random_light():
|
||||
random_pol = Vector([[np.random.uniform(0, 1)], [np.random.uniform(0, 1)]])
|
||||
random_pol = Vector(
|
||||
[[np.random.uniform(0, 1)], [np.random.uniform(0, 1)]])
|
||||
return normalize_state(random_pol)
|
||||
|
||||
def experiment(id, random_ls, filters):
|
||||
@ -1354,12 +1441,22 @@ def test_light():
|
||||
experiment(2, random_lights, [ver_filter, hor_filter])
|
||||
|
||||
# TODO: Something is wrong here...
|
||||
# Vertical after diagonal after horizontal - should result in ~ 50% compared to only Horizontal
|
||||
# Vertical after diagonal after horizontal - should result in ~ 50%
|
||||
# compared to only Horizontal
|
||||
experiment(3, random_lights, [ver_filter, diag_filter, hor_filter])
|
||||
|
||||
|
||||
def get_bin_fmt(count):
|
||||
return "{:0" + str(int(np.ceil(np.log2(count)))) + "b}"
|
||||
|
||||
|
||||
def generate_bin(i, count):
|
||||
format_str = get_bin_fmt(count)
|
||||
return format_str.format(i)
|
||||
|
||||
|
||||
def generate_bins(count):
|
||||
format_str = "{:0" + str(int(np.ceil(np.log2(count)))) + "b}"
|
||||
format_str = get_bin_fmt(count)
|
||||
return [format_str.format(i) for i in range(count)]
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user