def test_WGate():
nqubits = 2
basis_states = superposition_basis(nqubits)
assert qapply(WGate(nqubits)*basis_states) == basis_states
expected = ((2/sqrt(pow(2, nqubits)))*basis_states) - IntQubit(1, nqubits=nqubits)
assert qapply(WGate(nqubits)*IntQubit(1, nqubits=nqubits)) == expected
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_sympy__physics__quantum__grover__WGate():
from sympy.physics.quantum.grover import WGate
assert _test_args(WGate(1))