def qft_steps(N=1, swapping=True):
"""
Quantum Fourier Transform operator on N qubits returning the individual
steps as unitary matrices operating from left to right.
Parameters
----------
N: int
Number of qubits.
swap: boolean
Flag indicating sequence of swap gates to be applied at the end or not.
Returns
-------
U_step_list: list of qobj
List of Hadamard and controlled rotation gates implementing QFT.
"""
if N < 1:
raise ValueError("Minimum value of N can be 1")
U_step_list = []
if N == 1:
U_step_list.append(snot())
else:
for i in range(N):
for j in range(i):
U_step_list.append(
cphase(np.pi / (2**(i - j)), N, control=i, target=j))
U_step_list.append(snot(N, i))
if swapping is True:
for i in range(N // 2):
U_step_list.append(swap(N, [N - i - 1, i]))
return U_step_list
def qft_steps(N=1, swapping=True):
"""
Quantum Fourier Transform operator on N qubits returning the individual
steps as unitary matrices operating from left to right.
Parameters
----------
N: int
Number of qubits.
swap: boolean
Flag indicating sequence of swap gates to be applied at the end or not.
Returns
-------
U_step_list: list of qobj
List of Hadamard and controlled rotation gates implementing QFT.
"""
if N < 1:
raise ValueError("Minimum value of N can be 1")
U_step_list = []
if N == 1:
U_step_list.append(snot())
else:
for i in range(N):
for j in range(i):
U_step_list.append(cphase(np.pi/(2**(i-j)), N,
control=i, target=j))
U_step_list.append(snot(N, i))
if swapping == True:
for i in range(N//2):
U_step_list.append(swap(N, [N-i-1, i]))
return U_step_list
def test_qpt_snot():
"quantum process tomography for snot gate"
U_psi = snot()
U_rho = spre(U_psi) * spost(U_psi.dag())
N = 1
op_basis = [[qeye(2), sigmax(), 1j * sigmay(), sigmaz()] for i in range(N)]
# op_label = [["i", "x", "y", "z"] for i in range(N)]
chi1 = qpt(U_rho, op_basis)
chi2 = np.zeros((2 ** (2 * N), 2 ** (2 * N)), dtype=complex)
chi2[1, 1] = chi2[1, 3] = chi2[3, 1] = chi2[3, 3] = 0.5
assert_(norm(chi2 - chi1) < 1e-8)
def test_qpt_snot():
"quantum process tomography for snot gate"
U_psi = snot()
U_rho = spre(U_psi) * spost(U_psi.dag())
N = 1
op_basis = [[qeye(2), sigmax(), 1j * sigmay(), sigmaz()] for i in range(N)]
# op_label = [["i", "x", "y", "z"] for i in range(N)]
chi1 = qpt(U_rho, op_basis)
chi2 = np.zeros((2**(2 * N), 2**(2 * N)), dtype=complex)
chi2[1, 1] = chi2[1, 3] = chi2[3, 1] = chi2[3, 3] = 0.5
assert_(norm(chi2 - chi1) < 1e-8)
x = sigmax()
print(x)
print("\n")
ket_zero = qubit_states(N=1, states=[0])
print(ket_zero)
print("\n")
print(x * ket_zero)
print("\n")
print(tensor([identity(N=2), hadamard_transform(N=1)]))
print("\n")
print(snot(N=2, target=1))
print("\n")
print(swap(N=2, targets=[0, 1]))
print("\n")
print(cnot(N=2, control=0, target=1))
print("\n")
print(cnot(N=4, control=0, target=3))
print("\n")
print(hadamard_transform(N=2) * qubit_states(N=2, states=[0, 0]))
print("\n")
qc3 = QubitCircuit(N=3)
