def test_quantum_fourier():
assert QFT(0,3).decompose() == SwapGate(0,2)*HadamardGate(0)*CGate((0,), PhaseGate(1))\
*HadamardGate(1)*CGate((0,), TGate(2))*CGate((1,), PhaseGate(2))*HadamardGate(2)
assert IQFT(0,3).decompose() == HadamardGate(2)*CGate((1,), RkGate(2,-2))*CGate((0,),RkGate(2,-3))\
*HadamardGate(1)*CGate((0,), RkGate(1,-2))*HadamardGate(0)*SwapGate(0,2)
assert represent(QFT(0,3), nqubits=3)\
== Matrix([[exp(2*pi*I/8)**(i*j%8)/sqrt(8) for i in range(8)] for j in range(8)])
assert QFT(0, 4).decompose() #non-trivial decomposition
assert qapply(QFT(0,3).decompose()*Qubit(0,0,0)).expand() ==\
qapply(HadamardGate(0)*HadamardGate(1)*HadamardGate(2)*Qubit(0,0,0)).expand()
def period_find(a, N):
"""Finds the period of a in modulo N arithmetic
This is quantum part of Shor's algorithm.It takes two registers,
puts first in superposition of states with Hadamards so: |k>|0>
with k being all possible choices. It then does a controlled mod and
a QFT to determine the order of a.
"""
epsilon = .5
#picks out t's such that maintains accuracy within epsilon
t = int(2 * math.ceil(log(N, 2)))
# make the first half of register be 0's |000...000>
start = [0 for x in range(t)]
#Put second half into superposition of states so we have |1>x|0> + |2>x|0> + ... |k>x>|0> + ... + |2**n-1>x|0>
factor = 1 / sqrt(2**t)
qubits = 0
for i in range(2**t):
qbitArray = arr(i, t) + start
qubits = qubits + Qubit(*qbitArray)
circuit = (factor * qubits).expand()
#Controlled second half of register so that we have:
# |1>x|a**1 %N> + |2>x|a**2 %N> + ... + |k>x|a**k %N >+ ... + |2**n-1=k>x|a**k % n>
circuit = CMod(t, a, N) * circuit
#will measure first half of register giving one of the a**k%N's
circuit = apply_operators(circuit)
print "controlled Mod'd"
for i in range(t):
circuit = measure_partial_oneshot(circuit, i)
# circuit = measure(i)*circuit
# circuit = apply_operators(circuit)
print "measured 1"
#Now apply Inverse Quantum Fourier Transform on the second half of the register
circuit = apply_operators(QFT(t, t * 2).decompose() * circuit,
floatingPoint=True)
print "QFT'd"
for i in range(t):
circuit = measure_partial_oneshot(circuit, i + t)
# circuit = measure(i+t)*circuit
# circuit = apply_operators(circuit)
print circuit
if isinstance(circuit, Qubit):
register = circuit
elif isinstance(circuit, Mul):
register = circuit.args[-1]
else:
register = circuit.args[-1].args[-1]
print register
n = 1
answer = 0
for i in range(len(register) / 2):
answer += n * register[i + t]
n = n << 1
if answer == 0:
raise OrderFindingException(
"Order finder returned 0. Happens with chance %f" % epsilon)
#turn answer into r using continued fractions
g = getr(answer, 2**t, N)
print g
return g
def test_sympy__physics__quantum__qft__QFT():
from sympy.physics.quantum.qft import QFT
assert _test_args(QFT(0, 1))
def test_qft_represent():
c = QFT(0,3)
a = represent(c,nqubits=3)
b = represent(c.decompose(),nqubits=3)
assert a.evalf(prec=10) == b.evalf(prec=10)
def test_qft_represent():
c = QFT(0, 3)
a = represent(c, nqubits=3)
b = represent(c.decompose(), nqubits=3)
assert a.evalf(n=10) == b.evalf(n=10)