def test_CMod():
assert apply_operators(CMod(4, 2, 2)*Qubit(0,0,1,0,0,0,0,0)) ==\
Qubit(0,0,1,0,0,0,0,0)
assert apply_operators(CMod(5, 5, 7)*Qubit(0,0,1,0,0,0,0,0,0,0)) ==\
Qubit(0,0,1,0,0,0,0,0,1,0)
assert apply_operators(CMod(3, 2, 3)*Qubit(0,1,0,0,0,0)) ==\
Qubit(0,1,0,0,0,1)
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 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_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 apply_operators(QFT(0,3).decompose()*Qubit(0,0,0)).expand() ==\
apply_operators(HadamardGate(0)*HadamardGate(1)*HadamardGate(2)*Qubit(0,0,0)).expand()
def test_ugate():
"""Test the general UGate."""
a,b,c,d = symbols('abcd')
uMat = Matrix([[a,b],[c,d]])
# Test basic case where gate exists in 1-qubit space
u1 = UGate((0,), uMat)
assert represent(u1, nqubits = 1) == uMat
assert apply_operators(u1*Qubit('0')) == a*Qubit('0') + c*Qubit('1')
assert apply_operators(u1*Qubit('1')) == b*Qubit('0') + d*Qubit('1')
# Test case where gate exists in a larger space
u2 = UGate((1,), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\
qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cnot_gate():
"""Test the CNOT gate."""
circuit = CNotGate(1,0)
assert represent(circuit, nqubits=2) ==\
Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])
circuit = circuit*Qubit('111')
assert matrix_to_qubit(represent(circuit, nqubits=3)) ==\
apply_operators(circuit)
def test_ugate():
"""Test the general UGate."""
a, b, c, d = symbols('abcd')
uMat = Matrix([[a, b], [c, d]])
# Test basic case where gate exists in 1-qubit space
u1 = UGate((0, ), uMat)
assert represent(u1, nqubits=1) == uMat
assert apply_operators(u1 * Qubit('0')) == a * Qubit('0') + c * Qubit('1')
assert apply_operators(u1 * Qubit('1')) == b * Qubit('0') + d * Qubit('1')
# Test case where gate exists in a larger space
u2 = UGate((1, ), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\
qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cnot_gate():
"""Test the CNOT gate."""
circuit = CNotGate(1, 0)
assert represent(circuit, nqubits=2) ==\
Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])
circuit = circuit * Qubit('111')
assert matrix_to_qubit(represent(circuit, nqubits=3)) ==\
apply_operators(circuit)
def test_swap_gate():
"""Test the SWAP gate."""
swap_gate_matrix = Matrix(((1,0,0,0),(0,0,1,0),(0,1,0,0),(0,0,0,1)))
assert represent(SwapGate(1,0).decompose(), nqubits=2) == swap_gate_matrix
assert apply_operators(SwapGate(1,3)*Qubit('0010')) == Qubit('1000')
nqubits = 4
for i in range(nqubits):
for j in range(i):
assert represent(SwapGate(i,j), nqubits=nqubits) ==\
represent(SwapGate(i,j).decompose(), nqubits=nqubits)
def test_swap_gate():
"""Test the SWAP gate."""
swap_gate_matrix = Matrix(
((1, 0, 0, 0), (0, 0, 1, 0), (0, 1, 0, 0), (0, 0, 0, 1)))
assert represent(SwapGate(1, 0).decompose(), nqubits=2) == swap_gate_matrix
assert apply_operators(SwapGate(1, 3) * Qubit('0010')) == Qubit('1000')
nqubits = 4
for i in range(nqubits):
for j in range(i):
assert represent(SwapGate(i,j), nqubits=nqubits) ==\
represent(SwapGate(i,j).decompose(), nqubits=nqubits)
def test_ugate_cgate_combo():
"""Test a UGate/CGate combination."""
a,b,c,d = symbols('abcd')
uMat = Matrix([[a,b],[c,d]])
cMat = Matrix([[1,0,0,0],[0,1,0,0],[0,0,a,b],[0,0,c,d]])
# Test basic case where gate exists in 1-qubit space.
u1 = UGate((0,), uMat)
cu1 = CGate(1, u1)
assert represent(cu1, nqubits = 2) == cMat
assert apply_operators(cu1*Qubit('10')) == a*Qubit('10') + c*Qubit('11')
assert apply_operators(cu1*Qubit('11')) == b*Qubit('10') + d*Qubit('11')
assert apply_operators(cu1*Qubit('01')) == Qubit('01')
assert apply_operators(cu1*Qubit('00')) == Qubit('00')
# Test case where gate exists in a larger space.
u2 = UGate((1,), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\
qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cgate():
"""Test the general CGate."""
# Test single control functionality
CNOTMatrix = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1],
[0, 0, 1, 0]])
assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix
# Test multiple control bit functionality
ToffoliGate = CGate((1, 2), XGate(0))
assert represent(ToffoliGate, nqubits=3) == \
Matrix([[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],\
[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],\
[0,0,0,0,0,0,1,0]])
ToffoliGate = CGate((3, 0), XGate(1))
assert apply_operators(ToffoliGate*Qubit('1001')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4))
assert apply_operators(ToffoliGate*Qubit('0000')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4))
CYGate = CGate(1, YGate(0))
CYGate_matrix = Matrix(
((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, -I), (0, 0, I, 0)))
# Test 2 qubit controlled-Y gate decompose method.
assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix
CZGate = CGate(0, ZGate(1))
CZGate_matrix = Matrix(
((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, -1)))
assert apply_operators(CZGate * Qubit('11')) == -Qubit('11')
assert matrix_to_qubit(represent(CZGate*Qubit('11'),nqubits=2)) ==\
-Qubit('11')
# Test 2 qubit controlled-Z gate decompose method.
assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix
CPhaseGate = CGate(0, PhaseGate(1))
assert apply_operators(CPhaseGate*Qubit('11')) ==\
I*Qubit('11')
assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \
I*Qubit('11')
def test_ugate_cgate_combo():
"""Test a UGate/CGate combination."""
a, b, c, d = symbols('abcd')
uMat = Matrix([[a, b], [c, d]])
cMat = Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, a, b], [0, 0, c, d]])
# Test basic case where gate exists in 1-qubit space.
u1 = UGate((0, ), uMat)
cu1 = CGate(1, u1)
assert represent(cu1, nqubits=2) == cMat
assert apply_operators(cu1 *
Qubit('10')) == a * Qubit('10') + c * Qubit('11')
assert apply_operators(cu1 *
Qubit('11')) == b * Qubit('10') + d * Qubit('11')
assert apply_operators(cu1 * Qubit('01')) == Qubit('01')
assert apply_operators(cu1 * Qubit('00')) == Qubit('00')
# Test case where gate exists in a larger space.
u2 = UGate((1, ), uMat)
u2Rep = represent(u2, nqubits=2)
for i in range(4):
assert u2Rep*qubit_to_matrix(IntQubit(i,2)) ==\
qubit_to_matrix(apply_operators(u2*IntQubit(i,2)))
def test_cgate():
"""Test the general CGate."""
# Test single control functionality
CNOTMatrix = Matrix([[1,0,0,0],[0,1,0,0],[0,0,0,1],[0,0,1,0]])
assert represent(CGate(1, XGate(0)), nqubits=2) == CNOTMatrix
# Test multiple control bit functionality
ToffoliGate = CGate((1,2), XGate(0))
assert represent(ToffoliGate, nqubits=3) == \
Matrix([[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],\
[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1],\
[0,0,0,0,0,0,1,0]])
ToffoliGate = CGate((3,0), XGate(1))
assert apply_operators(ToffoliGate*Qubit('1001')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('1001'), nqubits=4))
assert apply_operators(ToffoliGate*Qubit('0000')) == \
matrix_to_qubit(represent(ToffoliGate*Qubit('0000'), nqubits=4))
CYGate = CGate(1, YGate(0))
CYGate_matrix = Matrix(((1,0,0,0),(0,1,0,0),(0,0,0,-I),(0,0,I,0)))
# Test 2 qubit controlled-Y gate decompose method.
assert represent(CYGate.decompose(), nqubits=2) == CYGate_matrix
CZGate = CGate(0, ZGate(1))
CZGate_matrix = Matrix(((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,-1)))
assert apply_operators(CZGate*Qubit('11')) == -Qubit('11')
assert matrix_to_qubit(represent(CZGate*Qubit('11'),nqubits=2)) ==\
-Qubit('11')
# Test 2 qubit controlled-Z gate decompose method.
assert represent(CZGate.decompose(), nqubits=2) == CZGate_matrix
CPhaseGate = CGate(0, PhaseGate(1))
assert apply_operators(CPhaseGate*Qubit('11')) ==\
I*Qubit('11')
assert matrix_to_qubit(represent(CPhaseGate*Qubit('11'), nqubits=2)) == \
I*Qubit('11')
def _apply_operator_Qubit(self, qubits, **options):
return apply_operators(self.decompose() * qubits)
def _apply_operator_Qubit(self, qubits, **options):
return apply_operators(self.decompose()*qubits)