def test_U3():
assert (np.allclose(U3(pi, 0, pi, zero), X(zero)))
assert (np.allclose(U3(pi, 0, pi, one), X(one)))
assert (np.allclose(U3(pi, 0, pi, s), X(s)))
assert (np.allclose(U3(pi, pi / 2, pi / 2, zero), Y(zero)))
assert (np.allclose(U3(pi, pi / 2, pi / 2, one), Y(one)))
assert (np.allclose(U3(pi, pi / 2, pi / 2, s), Y(s)))
def test_X():
assert (np.array_equal(X(zero), one))
assert (np.array_equal(X(one), zero))
assert (np.array_equal(X(X(zero)), zero))
assert (np.array_equal(X(X(one)), one))
assert (np.array_equal(X(s), np.array([[beta], [alpha]],
dtype=np.complex)))
assert (np.array_equal(X(X(s)), s))
def cond_phase_shift(circuit):
"""
Performs the conditional phase shift operation 2|0><0| - I on the given
circuit.
Parameters
----------
circuit : Circuit
Quantum circuit to apply the conditional phase shift operation on
Returns
-------
state : np.ndarray
State of the system after the application of the conditional phase
shift operation.
"""
n = circuit.num_rails
state = None
# First, invert all qubits
for i in range(1, n):
qubits = [
i,
]
gate = X.copy()
circuit.add_gate(gate, qubits)
# Then, apply a Z operation on any one qubit, with a control from all other
# input qubits. This will ensure that the state gets negated only when it
# is |111...1>
gate = Z.copy()
qubits = [
n - 1,
]
controls = range(1, n - 1)
circuit.add_gate(gate, qubits, controls)
# Finally, invert everything back, so that only |000...0> would have
# suffered negation
for i in range(1, n):
qubits = [
i,
]
gate = X.copy()
state = circuit.add_gate(gate, qubits)
return state
def oracle(circuit, M, targets):
"""
Constructs the oracle for Grover's search algorithm for a given set of
target states.
Parameters
----------
circuit : Circuit
Quantum circuit to add the oracle to
M : integer
Number of target states
targets : list of strings
List of target states (in binary) for the Grover's search algorithm
Returns
-------
state : np.ndarray
State of the system after the application of the oracle.
"""
state = None
n = circuit.num_rails
for target in targets:
qubits = [n,] # The last qubit of the oracle is flipped when the
# function is 1, and is not flipped when the
# function is 0 (y XOR f)
gate = X.copy()
t = np.array(list(target), dtype=int)
one_controls = np.where(t == 1)[0] + 1 # +1 since rails are numbered
# from 1 to n, not 0 to n-1
zero_controls = -1 * (np.where(t == 0)[0] + 1)
controls = np.hstack((one_controls, zero_controls))
state = circuit.add_gate(gate, qubits, controls)
return state
def cond_phase_shift(circuit):
"""
Performs the conditional phase shift operation 2|0><0| - I on the given
circuit.
Parameters
----------
circuit : Circuit
Quantum circuit to apply the conditional phase shift operation on
Returns
-------
state : np.ndarray
State of the system after the application of the conditional phase
shift operation.
"""
n = circuit.num_rails
state = None
# First, invert all qubits
for i in range(1, n):
qubits = [i,]
gate = X.copy()
circuit.add_gate(gate, qubits)
# Then, apply a Z operation on any one qubit, with a control from all other
# input qubits. This will ensure that the state gets negated only when it
# is |111...1>
gate = Z.copy()
qubits = [n-1,]
controls = range(1, n-1)
circuit.add_gate(gate, qubits, controls)
# Finally, invert everything back, so that only |000...0> would have
# suffered negation
for i in range(1, n):
qubits = [i,]
gate = X.copy()
state = circuit.add_gate(gate, qubits)
return state
def test_Z():
assert (np.allclose(Z(Z(s)), s))
assert (np.allclose(H(Z(H(zero))), X(zero)))
assert (np.allclose(H(Z(H(one))), X(one)))
assert (np.allclose(H(Z(H(s))), X(s)))
assert (np.allclose(H(X(H(zero))), Z(zero)))
assert (np.allclose(H(X(H(one))), Z(one)))
assert (np.allclose(H(X(H(s))), Z(s)))
def oracle(circuit, M, targets):
"""
Constructs the oracle for Grover's search algorithm for a given set of
target states.
Parameters
----------
circuit : Circuit
Quantum circuit to add the oracle to
M : integer
Number of target states
targets : list of strings
List of target states (in binary) for the Grover's search algorithm
Returns
-------
state : np.ndarray
State of the system after the application of the oracle.
"""
state = None
n = circuit.num_rails
for target in targets:
qubits = [
n,
] # The last qubit of the oracle is flipped when the
# function is 1, and is not flipped when the
# function is 0 (y XOR f)
gate = X.copy()
t = np.array(list(target), dtype=int)
one_controls = np.where(t == 1)[0] + 1 # +1 since rails are numbered
# from 1 to n, not 0 to n-1
zero_controls = -1 * (np.where(t == 0)[0] + 1)
controls = np.hstack((one_controls, zero_controls))
state = circuit.add_gate(gate, qubits, controls)
return state