def test_OracleGate():
v = OracleGate(1, lambda qubits: qubits == IntQubit(0))
assert qapply(v*IntQubit(0)) == -IntQubit(0)
assert qapply(v*IntQubit(1)) == IntQubit(1)
nbits = 2
v = OracleGate(2, return_one_on_two)
assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nbits)
assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nbits)
assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits)
assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits)
def main():
print()
print('Demonstration of Grover\'s Algorithm')
print('The OracleGate or V Gate carries the unknown function f(x)')
print(
'> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)')
print('> and 0 (False in our case) otherwise')
print()
nqubits = 2
print('nqubits = ', nqubits)
v = OracleGate(nqubits, black_box)
print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
print()
psi = superposition_basis(nqubits)
print('psi:')
pprint(psi)
demo_vgate_app(v)
print('qapply(v*psi)')
pprint(qapply(v * psi))
print()
w = WGate(nqubits)
print('WGate or w = WGate(%r)' % nqubits)
print('On a 2 Qubit system like psi, 1 iteration is enough to yield |1>')
print('qapply(w*v*psi)')
pprint(qapply(w * v * psi))
print()
nqubits = 3
print('On a 3 Qubit system, it requires 2 iterations to achieve')
print('|1> with high enough probability')
psi = superposition_basis(nqubits)
print('psi:')
pprint(psi)
v = OracleGate(nqubits, black_box)
print('Oracle or v = OracleGate(%r, black_box)' % nqubits)
print()
print('iter1 = grover.grover_iteration(psi, v)')
iter1 = qapply(grover_iteration(psi, v))
pprint(iter1)
print()
print('iter2 = grover.grover_iteration(iter1, v)')
iter2 = qapply(grover_iteration(iter1, v))
pprint(iter2)
print()
def main():
print()
print("Demonstration of Grover's Algorithm")
print("The OracleGate or V Gate carries the unknown function f(x)")
print(
"> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)")
print("> and 0 (False in our case) otherwise")
print()
nqubits = 2
print("nqubits = ", nqubits)
v = OracleGate(nqubits, black_box)
print("Oracle or v = OracleGate(%r, black_box)" % nqubits)
print()
psi = superposition_basis(nqubits)
print("psi:")
pprint(psi)
demo_vgate_app(v)
print("qapply(v*psi)")
pprint(qapply(v * psi))
print()
w = WGate(nqubits)
print("WGate or w = WGate(%r)" % nqubits)
print("On a 2 Qubit system like psi, 1 iteration is enough to yield |1>")
print("qapply(w*v*psi)")
pprint(qapply(w * v * psi))
print()
nqubits = 3
print("On a 3 Qubit system, it requires 2 iterations to achieve")
print("|1> with high enough probability")
psi = superposition_basis(nqubits)
print("psi:")
pprint(psi)
v = OracleGate(nqubits, black_box)
print("Oracle or v = OracleGate(%r, black_box)" % nqubits)
print()
print("iter1 = grover.grover_iteration(psi, v)")
iter1 = qapply(grover_iteration(psi, v))
pprint(iter1)
print()
print("iter2 = grover.grover_iteration(iter1, v)")
iter2 = qapply(grover_iteration(iter1, v))
pprint(iter2)
print()
def test_OracleGate():
v = OracleGate(1, lambda qubits: qubits == IntQubit(0))
assert qapply(v*IntQubit(0)) == -IntQubit(0)
assert qapply(v*IntQubit(1)) == IntQubit(1)
nbits = 2
v = OracleGate(2, return_one_on_two)
assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nqubits=nbits)
assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nqubits=nbits)
assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits)
assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits)
assert represent(OracleGate(1, lambda qubits: qubits == IntQubit(0)), nqubits=1) == \
Matrix([[-1, 0], [0, 1]])
assert represent(v, nqubits=2) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]])
def test_OracleGate():
v = OracleGate(1, lambda qubits: qubits == IntQubit(0))
assert qapply(v*IntQubit(0)) == -IntQubit(0)
assert qapply(v*IntQubit(1)) == IntQubit(1)
nbits = 2
v = OracleGate(2, return_one_on_two)
assert qapply(v*IntQubit(0, nbits)) == IntQubit(0, nbits)
assert qapply(v*IntQubit(1, nbits)) == IntQubit(1, nbits)
assert qapply(v*IntQubit(2, nbits)) == -IntQubit(2, nbits)
assert qapply(v*IntQubit(3, nbits)) == IntQubit(3, nbits)
# Due to a bug of IntQubit, this first assertion is buggy
# assert represent(OracleGate(1, lambda qubits: qubits == IntQubit(0)), nqubits=1) == \
# Matrix([[-1/sqrt(2), 0], [0, 1/sqrt(2)]])
assert represent(v, nqubits=2) == Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]])
def test_grover_iteration_2():
numqubits = 4
basis_states = superposition_basis(numqubits)
v = OracleGate(numqubits, return_one_on_two)
# After (pi/4)sqrt(pow(2, n)), IntQubit(2) should have highest prob
# In this case, after around pi times (3 or 4)
iterated = grover_iteration(basis_states, v)
iterated = qapply(iterated)
iterated = grover_iteration(iterated, v)
iterated = qapply(iterated)
iterated = grover_iteration(iterated, v)
iterated = qapply(iterated)
# In this case, probability was highest after 3 iterations
# Probability of Qubit('0010') was 251/256 (3) vs 781/1024 (4)
# Ask about measurement
expected = (-13*basis_states)/64 + 264*IntQubit(2, numqubits)/256
assert qapply(expected) == iterated
def test_grover_iteration_1():
numqubits = 2
basis_states = superposition_basis(numqubits)
v = OracleGate(numqubits, return_one_on_one)
expected = IntQubit(1, nqubits=numqubits)
assert qapply(grover_iteration(basis_states, v)) == expected
qcol.add(q4.qutuple)
qcol.add(q5.qutuple)
qcol.add(q6.qutuple)
qcol.add(q7.qutuple)
qcol.add(q8.qutuple)
f1 = lambda qubits: qubits == IntQubit(1)
f2 = lambda qubits: qubits == IntQubit(2)
f3 = lambda qubits: qubits == IntQubit(3)
f4 = lambda qubits: qubits == IntQubit(4)
f5 = lambda qubits: qubits == IntQubit(5)
f6 = lambda qubits: qubits == IntQubit(6)
f7 = lambda qubits: qubits == IntQubit(7)
f8 = lambda qubits: qubits == IntQubit(8)
v1 = OracleGate(q1.nQubits(), f1)
v2 = OracleGate(q2.nQubits(), f2)
v3 = OracleGate(q3.nQubits(), f3)
v4 = OracleGate(q4.nQubits(), f4)
v5 = OracleGate(q5.nQubits(), f5)
v6 = OracleGate(q6.nQubits(), f6)
v7 = OracleGate(q7.nQubits(), f7)
v8 = OracleGate(q8.nQubits(), f8)
print("Applied Oracle Gates:")
print(qapply(v1 * q1.qubit))
print(qapply(v2 * q2.qubit))
print(qapply(v3 * q3.qubit))
print(qapply(v4 * q4.qubit))
print(qapply(v5 * q5.qubit))
print(qapply(v6 * q6.qubit))
def test_sympy__physics__quantum__grover__OracleGate():
from sympy.physics.quantum.grover import OracleGate
assert _test_args(OracleGate())
