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 test_F_avg_psi(sqrt_SWAP_basis, canonical_basis):
F = krotov.functionals.F_avg(
fw_states_T=sqrt_SWAP_basis,
basis_states=canonical_basis,
gate=qutip_gates.cphase(np.pi),
)
assert abs(F - 0.3) < 1e-14
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 cphase_lv_full_objectives(canonical_basis):
L = qutip.Qobj() # dummy Liouvillian (won't be used)
return krotov.objectives.gate_objectives(
canonical_basis,
gate=qutip_gates.cphase(np.pi),
H=L,
liouville_states_set='full',
)
def test_F_avg_rho(sqrt_SWAP_basis, canonical_basis):
fw_states_T = [
psi * phi.dag()
for (psi, phi) in product(sqrt_SWAP_basis, sqrt_SWAP_basis)
]
F = krotov.functionals.F_avg(
fw_states_T=fw_states_T,
basis_states=canonical_basis,
gate=qutip_gates.cphase(np.pi),
)
assert abs(F - 0.3) < 1e-14
def cphase_objectives(canonical_basis):
H = qutip.Qobj() # dummy Hamiltonian (won't be used)
return krotov.objectives.gate_objectives(canonical_basis,
gate=qutip_gates.cphase(np.pi),
H=H)