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light experiment works

This commit is contained in:
Daniel Tsvetkov 2020-03-27 11:06:42 +01:00
parent 7bd12b203d
commit 4fd95fcbf6
4 changed files with 106 additions and 81 deletions
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2
06_krisis.py
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@ -2,7 +2,7 @@ import cirq
import numpy as np
from collections import defaultdict
from lib_q_computer_math import State, QuantumCircuit, QuantumProcessor, C, H, x, _, _0, _1
from lib import State, QuantumCircuit, QuantumProcessor, C, H, x, _, _0, _1
def from_angles_1(theta, phi):

2
compiler.py
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@ -1,4 +1,4 @@
from lib_q_computer_math import s
from lib import s
def int_to_state(i):

163
lib_q_computer_math.py → lib.py
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@ -2,6 +2,7 @@ import random
from collections import defaultdict
from functools import reduce
from numbers import Complex
from pprint import pprint
from typing import Union
import numpy as np
@ -46,6 +47,9 @@ class Matrix(object):
def __add__(self, other):
return Matrix(self.m + other.m)
def __sub__(self, other):
return Matrix(self.m - other.m)
def __eq__(self, other):
if isinstance(other, Complex):
return bool(np.allclose(self.m, other))
@ -86,8 +90,30 @@ class Matrix(object):
def __len__(self):
return len(self.m)
def inner(self, other):
"""Define inner product - a.k.a dot product, scalar product - <0|0>"""
return Matrix(np.dot(self._conjugate_transpose(), other.m))
def dot(self, other):
"""Alias to inner"""
return self.inner(other)
def scalar(self, other):
"""Alias to inner"""
return self.inner(other)
def outer(self, other):
"""Define outer product |0><0|"""
"""Define outer product |0><0|
https://en.wikipedia.org/wiki/Outer_product
Given two vectors u and v, their outer product u ⊗ v is defined
as the m × n matrix A obtained by multiplying each element of u
by each element of v
The outer product u ⊗ v is equivalent to a matrix multiplication uvT,
provided that u is represented as a m × 1 column vector and v as a
n × 1 column vector (which makes vT a row vector).
"""
return Matrix(np.outer(self.m, other.m))
def x(self, other):
@ -136,10 +162,16 @@ class Vector(Matrix):
return self.m.shape[1] == 1
VectorOrList = Union[Vector, ListOrNdarray]
class State(Vector):
def __init__(self, m: ListOrNdarray = None, name: str = '', *args, **kwargs):
def __init__(self, m: VectorOrList = None, name: str = '', *args, **kwargs):
"""State vector representing quantum state"""
super().__init__(m, *args, **kwargs)
if type(m) is Vector:
super().__init__(m.m, *args, **kwargs)
else:
super().__init__(m, *args, **kwargs)
self.name = name
self.measurement_result = None
# TODO: SHOULD WE NORMALIZE?
@ -190,6 +222,9 @@ class State(Vector):
assert 0 <= phi <= 2 * np.pi
return theta, phi
def to_ket(self):
return self.conjugate_transpose()
def rotate_x(self, theta):
return Rx(theta).on(self)
@ -276,7 +311,7 @@ class State(Vector):
Measures with a measurement operator mo
TODO: Can't define `mo: MeasurementOperator` because in python you can't declare classes before defining them
"""
m = mo.on(self) / np.sqrt(mo.get_prob(self))
m = mo.on(self).m / np.sqrt(mo.get_prob(self))
return State(m)
def measure_partial(self, qubit_n):
@ -342,7 +377,7 @@ class State(Vector):
def test_measure_partial():
state = b_00
state = b_phi_p
state.measure_partial(1)
@ -635,31 +670,31 @@ _m = State([[1 / np.sqrt(2)],
name='-')
# 4 Bell states
b_00 = State([[1 / np.sqrt(2)],
[0],
[0],
[1 / np.sqrt(2)]],
name='B00')
b_phi_p = State([[1 / np.sqrt(2)],
[0],
[0],
[1 / np.sqrt(2)]],
name="{}+".format(REPR_GREEK_PHI))
b_01 = State([[0],
[1 / np.sqrt(2)],
[1 / np.sqrt(2)],
[0]],
name='B01')
b_psi_p = State([[0],
[1 / np.sqrt(2)],
[1 / np.sqrt(2)],
[0]],
name="{}+".format(REPR_GREEK_PSI))
b_10 = State([[1 / np.sqrt(2)],
[0],
[0],
[-1 / np.sqrt(2)]],
name='B10')
b_phi_m = State([[1 / np.sqrt(2)],
[0],
[0],
[-1 / np.sqrt(2)]],
name="{}-".format(REPR_GREEK_PHI))
b_11 = State([[0],
[1 / np.sqrt(2)],
[-1 / np.sqrt(2)],
[0]],
name='B11')
b_psi_m = State([[0],
[1 / np.sqrt(2)],
[-1 / np.sqrt(2)],
[0]],
name="{}-".format(REPR_GREEK_PSI))
well_known_states = [_p, _m, b_00, b_01, b_10, b_11]
well_known_states = [_p, _m, b_phi_p, b_psi_p, b_phi_m, b_psi_m]
_ = I = UnitaryOperator([[1, 0],
[0, 1]],
@ -847,17 +882,17 @@ def test():
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 _0 | _0 == 1 # parallel have 1 product
assert _0 | _1 == 0 # orthogonal have 0 product
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 | (8 * _0) == 8 * (_1 | _0) # Inner product is linear multiplied by constants
assert _p | (_1 + _0) == (_p | _1) + (_p | _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(_0.length(), 1.0)
assert np.isclose(_p.length(), 1.0)
assert _0 | _1 == (_1 | _0).complex_conjugate() # non-commutative inner product
assert _0.inner(_1) == _1.inner(_0).complex_conjugate() # non-commutative inner product
test_to_from_angles()
@ -871,14 +906,14 @@ def test():
test_unitary_hermitian()
# Pauli X gate flips the |0> to |1> and the |1> to |0>
assert X | _1 == _0
assert X | _0 == _1
assert X.on(_1) == _0
assert X.on(_0) == _1
# Test the Y Pauli operator with complex number literal notation
assert Y | _0 == State([[0],
[1j]])
assert Y | _1 == State([[-1j],
[0]])
assert Y.on(_0) == State([[0],
[1j]])
assert Y.on(_1) == State([[-1j],
[0]])
# Test Pauli rotation gates
testRotPauli()
@ -928,11 +963,11 @@ def test():
# First - create a superposition
H = UnitaryOperator([[1 / np.sqrt(2), 1 / np.sqrt(2)],
[1 / np.sqrt(2), -1 / np.sqrt(2)], ])
superpos = H | _0
superpos = H.on(_0)
assert superpos == _p
# Then CNOT the superposition with a |0> qubit
bell = CNOT | (superpos * _0)
bell = CNOT.on(superpos * _0)
assert bell == State([[1 / np.sqrt(2)],
[0.],
[0.],
@ -944,7 +979,6 @@ def test():
assert np.isclose(bell.get_prob(0b11), 0.5) # Probability for bell in 11 is 0.5
################################
# TODO: Don't know where outer product fits - something about density operator?
assert _0.x(_0) == Matrix([[1, 0],
[0, 0]])
assert _0.x(_1) == Matrix([[0, 1],
@ -1196,33 +1230,44 @@ def test_quantum_processor():
def test_light():
# http://alienryderflex.com/polarizer/
# TODO: Are these measurement operators the correct way to represent hor/ver/diag filter?
# No, becuase they are not unitaries
hor_filter = MeasurementOperator.create_from_prob(Matrix(_0.m), name='h')
diag_filter = MeasurementOperator.create_from_prob(Matrix(_p.m), name='d')
ver_filter = MeasurementOperator.create_from_prob(Matrix(_1.m), name='v')
# create random light/photon
random_pol = Vector([[np.random.uniform(0, 1)], [np.random.uniform(0, 1)]])
random_light = normalize_state(random_pol)
def random_light():
random_pol = Vector([[np.random.uniform(0, 1)], [np.random.uniform(0, 1)]])
return normalize_state(random_pol)
# TODO: Doesn't work...
qc = QuantumCircuit(1, initial_steps=[[random_light]])
qc.add_row([hor_filter, ver_filter])
qc.print()
qp = QuantumProcessor(qc)
qp.print_sample(qp.get_sample(100))
def experiment(id, random_ls, filters):
total_light = defaultdict(int)
human_state = "Light"
for filter in filters:
human_state += "->{}".format(filter.name)
# add three filters as operators
qc = QuantumCircuit(1, initial_steps=[[random_light]])
qc.add_row([hor_filter, diag_filter, ver_filter])
qc.print()
qp = QuantumProcessor(qc)
qp.print_sample(qp.get_sample(100))
for r in random_ls:
st = filters[0].on(r)
for filter in filters:
st = filter.on(st)
st = State(st)
total_light[st.measure()] += 1
print("{}. {}:\n {}".format(id, human_state, dict(total_light)))
its = 100
random_lights = [random_light() for _ in range(its)]
# Just horizonal - should result in some light
experiment(1, random_lights, [hor_filter, ])
# Vertical after horizonal - should result in 0
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
experiment(3, random_lights, [ver_filter, diag_filter, hor_filter])
if __name__ == "__main__":
test()
# test_quantum_processor()
# test_light()
test_quantum_processor()
test_light()
# test_measure_partial()

20
play.py
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@ -1,20 +0,0 @@
import numpy as np
from lib_q_computer_math import Vector, Matrix, MeasurementOperator, _0, _1, _p, normalize_state, State
def main():
random_pol = Vector([[np.random.uniform(0, 1)], [np.random.uniform(0, 1)]])
random_light = normalize_state(random_pol)
hor_filter = MeasurementOperator.create_from_prob(Matrix(_0.m), name='h')
diag_filter = MeasurementOperator.create_from_prob(Matrix(_p.m), name='d')
ver_filter = MeasurementOperator.create_from_prob(Matrix(_1.m), name='v')
State(hor_filter.on(random_light).m).measure()
print(hor_filter.on(_0))
print(ver_filter.on(_0))
print(ver_filter.on(hor_filter.on(_0)))
print(ver_filter.on(diag_filter.on(hor_filter.on(_0))))
print()
if __name__ == "__main__":
main()