def test_xgate(self):
"""XGATE: Flip along √i axis. 1 => 0, 0 => 1"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
cnot_tests = [
['Verify XGATE +|0>| = +|1>',
self.xgate(z), o],
['Verify XGATE +|1>| = +|0>',
self.xgate(o), z],
['Verify XGATE -|0>| = -|1>',
self.xgate(-z), -o],
['Verify XGATE -|1>| = -|0>',
self.xgate(-o), -z],
['Verify XGATE |00>| = |10>',
self.xgate(zz), oz],
['Verify XGATE |01>| =-|11>',
self.xgate(zo), -oo],
['Verify XGATE |10>| = |10>',
self.xgate(oz), zz],
['Verify XGATE |11>| = |01>',
self.xgate(oo), zo],
]
for test in cnot_tests:
title, calc, expect = test
self.assertEqual(calc, expect)
def test_16_steps(self):
"""16 Step Circle Walk test"""
z = Construct((1, 0))
steps = [
(0, 1),
(sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), sqrt(1 / 2)),
(0, -1),
(-1, 0),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-1, 0),
(0, -1),
(-sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), -sqrt(1 / 2)),
(0, 1),
(1, 0),
(sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), sqrt(1 / 2)),
(1, 0),
]
starting = Construct((z.flat()))
for i in range(16):
if i % 2:
gate = 'Hadamard'
z2 = self.hadamard(z)
else:
gate = ' XGate'
z2 = self.xgate(z)
z = z2
self.assertEqual(z, Construct(steps[i]))
self.assertEqual(z, starting)
def test_hadamard(self):
"""Hadamard gate test"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
hadamard_tests = [
['Verify HADAMARD +| 0>| = + | +>',
self.hadamard(z), rz],
['Verify HADAMARD +| 1>| = + | ->',
self.hadamard(o), ro],
['Verify HADAMARD -| 0>| = - | +>',
self.hadamard(-z), -rz],
['Verify HADAMARD -| 1>| = - | ->',
self.hadamard(-o), -ro],
[
'Verify HADAMARD +|00>| = + |1+>',
self.hadamard(zz),
rz.tensor(z)
],
[
'Verify HADAMARD +|01>| = - |11>',
self.hadamard(zo), -rz.tensor(o)
],
[
'Verify HADAMARD +|10>| = + |00>',
self.hadamard(oz),
ro.tensor(z)
],
[
'Verify HADAMARD +|11>| = + |01>',
self.hadamard(oo),
ro.tensor(o)
],
]
for test in hadamard_tests:
title, calc, expected = test
self.assertEqual(calc, expected)
def test_octonion_dimensions(self):
"""Check that a number intended to be a octonion says that it is"""
for n in range(self.LOOPS):
z = Construct([random() for _ in range(8)])
self.assertFalse(z.is_complex())
self.assertFalse(z.is_quaternion())
self.assertTrue(z.is_octonion())
self.assertFalse(z.is_sedenion())
self.assertNotEqual(z.dimension(), 32)
def test_32ion(self):
"""Check that a number intended to be 32 dimensional knows that it is"""
for n in range(self.LOOPS):
z = Construct([random() for _ in range(32)])
self.assertFalse(z.is_complex())
self.assertFalse(z.is_quaternion())
self.assertFalse(z.is_octonion())
self.assertFalse(z.is_sedenion())
self.assertEqual(z.dimension(), 32)
def test_constant_0(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = Construct(z.flat())
target = Construct(z.flat())
self.assertEqual(control, z)
self.assertEqual(target, z)
control = Construct(o.flat())
target = Construct(z.flat())
self.assertEqual(control, o)
self.assertEqual(target, z)
def test_identity(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, z)
self.assertEqual(target, z)
control = o.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, o)
self.assertEqual(target, z)
def test_constant_1(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, z)
self.assertEqual(target, o)
control = o.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, o)
self.assertEqual(target, o)
def test_tensor(self):
z1 = Construct((1, 2))
z2 = Construct((3, 4))
z = Construct((1, 0))
o = Construct((0, 1))
brakets = [
[z1.tensor(z2), (3, 4, 6, 8)],
[o.tensor(z.tensor(z)), (0, 0, 0, 0, 1, 0, 0, 0)],
[o.tensor(z.tensor(o)), (0, 0, 0, 0, 0, 1, 0, 0)],
[o.tensor(o.tensor(z)), (0, 0, 0, 0, 0, 0, 1, 0)],
[o.tensor(o.tensor(o)), (0, 0, 0, 0, 0, 0, 0, 1)],
[
o.tensor(z.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
]
for item in brakets:
calc, expected = item
expect = Construct(expected)
self.assertEqual(calc, expect)