def test_correlations(self):
tests = [ # stabilizers
["ZI", "IZ"],
["ZZ", "XX"],
["ZX", "XZ"],
["XXX", "ZZI", "IZZ"],
["XIII", "IXII", "IIXI", "IIIX"],
["XZII", "ZXZI", "IZXZ", "IIZX"], # line graph
["XZIZ", "ZXZI", "IZXZ", "ZIZX"], # cycle graph
["XZZZ", "ZXZZ", "ZZXZ", "ZZZX"], # complete graph
["XZZZ", "ZXII", "ZIXI", "ZIIX"], # star graph
]
for stabilizers in tests:
for stabilizer in stabilizers:
for _ in range(10):
with self.subTest(stabilizers=stabilizers,
stabilizer=stabilizer):
s = StabilizerState(stabilizers)
outcomes = []
qubit = 0
for pauli in stabilizer:
if pauli == 'X':
s.apply_H(qubit)
elif pauli == 'Y':
s.apply_K(qubit)
elif pauli == 'Z':
pass
else:
qubit += 1
continue
outcomes.append(s.measure(qubit))
self.assertEqual(sum(outcomes) % 2, 0)
def test_going_to_graph(self):
one_Bell_pair = StabilizerState(["-1XX", "+1ZZ"])
G = nx.Graph()
G.add_edge(0, 1)
one_Bell_pair_graph = one_Bell_pair.find_SQC_equiv_graph_state()
self.assertTrue(G, one_Bell_pair_graph)
two_EPR_pairs = StabilizerState([[1, 0, 0, 1, 0, 0, 0, 0],
[0, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 1],
[0, 0, 0, 0, 0, 1, 1, 0]])
G.remove_edge(0, 1)
G.add_edges_from([(0, 3), (1, 2)])
two_EPR_pairs_graph = two_EPR_pairs.find_SQC_equiv_graph_state()
self.assertTrue(G, two_EPR_pairs_graph)
n = 5
GHZ = StabilizerState(n)
GHZ.apply_H(0)
for i in range(1, n):
GHZ.apply_CNOT(0, i)
GHZ_graph, operations = GHZ.find_SQC_equiv_graph_state(
return_operations=True)
self.assertTrue(GHZ_graph, nx.star_graph(n - 1))
self.assertTrue(operations == [("H", i) for i in range(1, n)])
def test_GHZ(self):
n = 5
for _ in range(20):
GHZ = StabilizerState(n)
GHZ.apply_H(0)
for i in range(1, n):
GHZ.apply_CNOT(0, i)
outcomes = [GHZ.measure(0) for _ in range(n)]
self.assertNotIn(False,
[outcomes[0] == outcomes[i] for i in range(1, n)])
def test_apply_CZ(self):
# Classical CNOT
z0x0 = StabilizerState([[0, 0, 1, 0], [0, 1, 0, 0]])
z1x1 = StabilizerState([[0, 0, 1, 0, 1], [0, 1, 0, 0, 1]])
z0x0.apply_X(0)
z0x0.apply_CZ(0, 1)
z0x0.put_in_standard_form()
self.assertTrue(z0x0 == z1x1)
# EPR pair
z0z0 = StabilizerState([[0, 0, 1, 0], [0, 0, 0, 1]])
epr = StabilizerState([[1, 1, 0, 0], [0, 0, 1, 1]])
z0z0.apply_H(0)
# Effective CNOT
z0z0.apply_H(1)
z0z0.apply_CZ(0, 1)
z0z0.apply_H(1)
self.assertTrue(z0z0 == epr)
# Graph state
z0z0 = StabilizerState([[0, 0, 1, 0], [0, 0, 0, 1]])
graph_state = StabilizerState([[1, 0, 0, 1], [0, 1, 1, 0]])
z0z0.apply_H(0)
z0z0.apply_H(1)
# Effective CPHASE
z0z0.apply_CZ(0, 1)
self.assertTrue(z0z0 == graph_state)
def test_apply_CNOT(self):
# Classical CNOT
z0z0 = StabilizerState([[0, 0, 1, 0], [0, 0, 0, 1]])
z1z1 = StabilizerState([[0, 0, 1, 0, 1], [0, 0, 0, 1, 1]])
z0z0.apply_X(0)
z0z0.apply_CNOT(0, 1)
self.assertTrue(z0z0 == z1z1)
# EPR pair
z0z0 = StabilizerState([[0, 0, 1, 0], [0, 0, 0, 1]])
epr = StabilizerState([[1, 1, 0, 0], [0, 0, 1, 1]])
z0z0.apply_H(0)
z0z0.apply_CNOT(0, 1)
self.assertTrue(z0z0 == epr)
# Graph state
z0z0 = StabilizerState([[0, 0, 1, 0], [0, 0, 0, 1]])
graph_state = StabilizerState([[1, 0, 0, 1], [0, 1, 1, 0]])
z0z0.apply_H(0)
z0z0.apply_H(1)
# Effective CPHASE
z0z0.apply_H(1)
z0z0.apply_CNOT(0, 1)
z0z0.apply_H(1)
self.assertTrue(z0z0 == graph_state)
def test_networkx_init(self):
n = 5
G = nx.complete_graph(n)
graph_state = StabilizerState(G)
self.assertEqual(graph_state.num_qubits, n)
# Create a star graph state and check that this is SQC equiv to the GHZ state
G = nx.star_graph(n - 1)
graph_state = StabilizerState(G)
for i in range(1, n):
graph_state.apply_H(i)
GHZ_state = StabilizerState(n)
GHZ_state.apply_H(0)
for i in range(1, n):
GHZ_state.apply_CNOT(0, i)
self.assertTrue(graph_state == GHZ_state)
def test_apply_H(self):
s1 = StabilizerState([[0, 1]])
s2 = StabilizerState([[1, 0]])
s3 = StabilizerState([[0, 1]])
s4 = StabilizerState([[1, 1]])
s5 = StabilizerState([[1, 1, 1]])
s1.apply_H(0)
self.assertTrue(s1 == s2)
s1.apply_H(0)
self.assertTrue(s1 == s3)
s4.apply_H(0)
self.assertTrue(s4 == s5)
class stabilizerEngine(quantumEngine):
"""
Basic quantum engine which uses stabilizer formalism. Thus only Clifford operations can be performed
Attributes:
maxQubits: maximum number of qubits this engine will support.
"""
def __init__(self, node, num, maxQubits=10):
"""
Initialize the simple engine. If no number is given for maxQubits, the assumption will be 10.
"""
super().__init__(node=node, num=num, maxQubits=maxQubits)
self.qubitReg = StabilizerState()
@property
def activeQubits(self):
return self.qubitReg.num_qubits
def add_fresh_qubit(self):
"""
Add a new qubit initialized in the \|0\> state.
"""
# Check if we are still allowed to add qubits
if self.activeQubits >= self.maxQubits:
raise noQubitError("No more qubits available in register.")
num = self.activeQubits
# Prepare a clean qubit state in |0>
self.qubitReg.add_qubit()
return num
def add_qubit(self, newQubit):
"""
Add new qubit in the state described by the array containing the generators of the stabilizer group.
This should be in the form required by the StabilizerState class.
"""
# Create the qubit
try:
qubit = StabilizerState(newQubit)
except Exception:
raise ValueError(
"'newQubits' was not in the correct form to be given as an argument to StabilizerState"
)
num = self.activeQubits
self.qubitReg = self.qubitReg.tensor_product(qubit)
return num
def remove_qubit(self, qubitNum):
"""
Removes the qubit with the desired number qubitNum
"""
if (qubitNum + 1) > self.activeQubits:
raise quantumError("No such qubit to remove")
self.measure_qubit(qubitNum)
def get_register_RI(self):
"""
Retrieves the entire register in real and imaginary part. Twisted only likes to send real valued lists,
not complex ones.
Since this is in stabilizer formalism the real part will be the boolean matrix describing the generators
and the imaginary part will be None
"""
Re = self.qubitReg.to_array().tolist()
Im = None
return Re, Im
def apply_H(self, qubitNum):
"""
Applies a Hadamard gate to the qubits with number qubitNum.
"""
self.qubitReg.apply_H(qubitNum)
def apply_K(self, qubitNum):
"""
Applies a K gate to the qubits with number qubitNum. Maps computational basis to Y eigenbasis.
"""
self.qubitReg.apply_K(qubitNum)
def apply_X(self, qubitNum):
"""
Applies a X gate to the qubits with number qubitNum.
"""
self.qubitReg.apply_X(qubitNum)
def apply_Z(self, qubitNum):
"""
Applies a Z gate to the qubits with number qubitNum.
"""
self.qubitReg.apply_Z(qubitNum)
def apply_Y(self, qubitNum):
"""
Applies a Y gate to the qubits with number qubitNum.
"""
self.qubitReg.apply_Y(qubitNum)
def apply_T(self, qubitNum):
"""
Applies a T gate to the qubits with number qubitNum.
"""
raise SimUnsupportedError(
"Cannot apply T gate in stabilizer formalism")
def apply_rotation(self, qubitNum, n, a):
"""
Applies a rotation around the axis n with the angle a to qubit with number qubitNum. If n is zero a ValueError
is raised.
:param qubitNum: int
Qubit number
:param n: tuple of floats
A tuple of three numbers specifying the rotation axis, e.g n=(1,0,0)
:param a: float
The rotation angle in radians.
"""
raise SimUnsupportedError(
"Cannot apply arbitrary rotation gate in stabilizer formalism")
def apply_CNOT(self, qubitNum1, qubitNum2):
"""
Applies the CNOT to the qubit with the numbers qubitNum1 and qubitNum2.
"""
self.qubitReg.apply_CNOT(qubitNum1, qubitNum2)
def apply_CPHASE(self, qubitNum1, qubitNum2):
"""
Applies the CPHASE to the qubit with the numbers qubitNum1 and qubitNum2.
"""
self.qubitReg.apply_CZ(qubitNum1, qubitNum2)
def apply_onequbit_gate(self, gate, qubitNum):
"""
Applies a unitary gate to the specified qubit.
Arguments:
gate The project Q gate to be applied
qubitNum the number of the qubit this gate is applied to
"""
raise SimUnsupportedError(
"Cannot apply arbitrary one qubit gate in stabilizer formalism")
def apply_twoqubit_gate(self, gate, qubit1, qubit2):
"""
Applies a unitary gate to the two specified qubits.
Arguments:
gate The project Q gate to be applied
qubit1 the first qubit
qubit2 the second qubit
"""
raise SimUnsupportedError(
"Cannot apply arbitrary two qubit gate in stabilizer formalism")
def measure_qubit_inplace(self, qubitNum):
"""
Measures the desired qubit in the standard basis. This returns the classical outcome. The quantum register
is in the post-measurment state corresponding to the obtained outcome.
Arguments:
qubitNum qubit to be measured
"""
# Check we have such a qubit...
if (qubitNum + 1) > self.activeQubits:
raise quantumError("No such qubit to be measured.")
outcome = self.qubitReg.measure(qubitNum, inplace=True)
# return measurement outcome
return outcome
def measure_qubit(self, qubitNum):
"""
Measures the desired qubit in the standard basis. This returns the classical outcome and deletes the qubit.
Arguments:
qubitNum qubit to be measured
"""
outcome = self.qubitReg.measure(qubitNum, inplace=False)
return outcome
def replace_qubit(self, qubitNum, state):
"""
Replaces the qubit at position qubitNum with the one given by state.
"""
raise NotImplementedError(
"Currently you cannot replace a qubit using stabilizer formalism")
def absorb(self, other):
"""
Absorb the qubits from the other engine into this one. This is done by tensoring the state at the end.
"""
# Check whether there is space
newNum = self.activeQubits + other.activeQubits
if newNum > self.maxQubits:
raise quantumError(
"Cannot merge: qubits exceed the maximum available.\n")
self.qubitReg = self.qubitReg.tensor_product(other.qubitReg)
def absorb_parts(self, R, I, activeQ):
"""
Absorb the qubits, given in pieces
Arguments:
R The array describing the stabilizer state (from StabilizerState.to_array)
I Unused
activeQ active number of qubits
"""
# Check whether there is space
newNum = self.activeQubits + activeQ
if newNum > self.maxQubits:
raise quantumError(
"Cannot merge: qubits exceed the maximum available.\n")
self.qubitReg = self.qubitReg.tensor_product(StabilizerState(R))