def pro_avfid_superoperator_compsubspace(U, L1):
"""
Average process (gate) fidelity in the qubit computational subspace for two qutrits
Leakage has to be taken into account, see Woods & Gambetta
"""
if U.type == 'oper':
inner = U.dag() * U_target
part_idx = [0, 1, 3, 4] # only computational subspace
ptrace = 0
for i in part_idx:
ptrace += inner[i, i]
dim = 4 # 2 qubits comp subspace
return np.real(
((np.abs(ptrace))**2 + dim * (1 - L1)) / (dim * (dim + 1)))
elif U.type == 'super':
kraus_form = qtp.to_kraus(U)
dim = 4 # 2 qubits in the computational subspace
part_idx = [0, 1, 3, 4] # only computational subspace
psum = 0
for A_k in kraus_form:
ptrace = 0
inner = U_target_diffdims.dag(
) * A_k # otherwise dimension mismatch
for i in part_idx:
ptrace += inner[i, i]
psum += (np.abs(ptrace))**2
return np.real((dim * (1 - L1) + psum) / (dim * (dim + 1)))
def pro_avfid_superoperator_compsubspace(U, L1):
"""
Average process (gate) fidelity in the qubit computational subspace for two qutrits.
Leakage has to be taken into account, see Woods & Gambetta.
The function assumes that the computational subspace (:= the 4 energy levels chosen as the two qubits) is given by
the standard basis |0> /otimes |0>, |0> /otimes |1>, |1> /otimes |0>, |1> /otimes |1>.
If this is not the case, one need to change the basis to that one, before calling this function.
"""
if U.type == 'oper':
inner = U.dag() * U_target
part_idx = [0, 1, 3, 4] # only computational subspace
ptrace = 0
for i in part_idx:
ptrace += inner[i, i]
dim = 4 # 2 qubits comp subspace
return np.real(
((np.abs(ptrace))**2 + dim * (1 - L1)) / (dim * (dim + 1)))
elif U.type == 'super':
kraus_form = qtp.to_kraus(U)
dim = 4 # 2 qubits in the computational subspace
part_idx = [0, 1, 3, 4] # only computational subspace
psum = 0
for A_k in kraus_form:
ptrace = 0
inner = U_target_diffdims.dag(
) * A_k # otherwise dimension mismatch
for i in part_idx:
ptrace += inner[i, i]
psum += (np.abs(ptrace))**2
return np.real((dim * (1 - L1) + psum) / (dim * (dim + 1)))
def pro_avfid_superoperator_compsubspace_phasecorrected(U, L1, phases):
"""
Average process (gate) fidelity in the qubit computational subspace for two qutrits
Leakage has to be taken into account, see Woods & Gambetta
The phase is corrected with Z rotations considering both transmons as qubits. The correction is done perfectly.
The function assumes that the computational subspace (:= the 4 energy levels chosen as the two qubits) is given by
the standard basis |0> /otimes |0>, |0> /otimes |1>, |1> /otimes |0>, |1> /otimes |1>.
If this is not the case, one need to change the basis to that one, before calling this function.
"""
Ucorrection = qtp.Qobj(
[[np.exp(-1j * np.deg2rad(phases[0])), 0, 0, 0, 0, 0, 0, 0, 0],
[0, np.exp(-1j * np.deg2rad(phases[1])), 0, 0, 0, 0, 0, 0, 0],
[0, 0, np.exp(-1j * np.deg2rad(phases[0])), 0, 0, 0, 0, 0, 0],
[0, 0, 0, np.exp(-1j * np.deg2rad(phases[2])), 0, 0, 0, 0, 0],
[
0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[3] - phases[-1])), 0, 0, 0, 0
], [0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[2])), 0, 0, 0],
[0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[0])), 0, 0],
[0, 0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[1])), 0],
[0, 0, 0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[0]))]],
type='oper',
dims=[[3, 3], [3, 3]])
if U.type == 'oper':
U = Ucorrection * U
inner = U.dag() * U_target
part_idx = [0, 1, 3, 4] # only computational subspace
ptrace = 0
for i in part_idx:
ptrace += inner[i, i]
dim = 4 # 2 qubits comp subspace
return np.real(
((np.abs(ptrace))**2 + dim * (1 - L1)) / (dim * (dim + 1)))
elif U.type == 'super':
U = qtp.to_super(Ucorrection) * U
kraus_form = qtp.to_kraus(U)
dim = 4 # 2 qubits in the computational subspace
part_idx = [0, 1, 3, 4] # only computational subspace
psum = 0
for A_k in kraus_form:
ptrace = 0
inner = U_target_diffdims.dag(
) * A_k # otherwise dimension mismatch
for i in part_idx:
ptrace += inner[i, i]
psum += (np.abs(ptrace))**2
return np.real((dim * (1 - L1) + psum) / (dim * (dim + 1)))
def pro_avfid_superoperator_compsubspace_phasecorrected(U, L1, phases):
"""
Average process (gate) fidelity in the qubit computational subspace for two qutrits
Leakage has to be taken into account, see Woods & Gambetta
The phase is corrected with Z rotations considering both transmons as qubits
"""
Ucorrection = qtp.Qobj(
[[np.exp(-1j * np.deg2rad(phases[0])), 0, 0, 0, 0, 0, 0, 0, 0],
[0, np.exp(-1j * np.deg2rad(phases[1])), 0, 0, 0, 0, 0, 0, 0],
[0, 0, np.exp(-1j * np.deg2rad(phases[0])), 0, 0, 0, 0, 0, 0],
[0, 0, 0, np.exp(-1j * np.deg2rad(phases[2])), 0, 0, 0, 0, 0],
[
0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[3] - phases[-1])), 0, 0, 0, 0
], [0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[2])), 0, 0, 0],
[0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[0])), 0, 0],
[0, 0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[1])), 0],
[0, 0, 0, 0, 0, 0, 0, 0,
np.exp(-1j * np.deg2rad(phases[0]))]],
type='oper',
dims=[[3, 3], [3, 3]])
if U.type == 'oper':
U = Ucorrection * U
inner = U.dag() * U_target
part_idx = [0, 1, 3, 4] # only computational subspace
ptrace = 0
for i in part_idx:
ptrace += inner[i, i]
dim = 4 # 2 qubits comp subspace
return np.real(
((np.abs(ptrace))**2 + dim * (1 - L1)) / (dim * (dim + 1)))
elif U.type == 'super':
U = qtp.to_super(Ucorrection) * U
kraus_form = qtp.to_kraus(U)
dim = 4 # 2 qubits in the computational subspace
part_idx = [0, 1, 3, 4] # only computational subspace
psum = 0
for A_k in kraus_form:
ptrace = 0
inner = U_target_diffdims.dag(
) * A_k # otherwise dimension mismatch
for i in part_idx:
ptrace += inner[i, i]
psum += (np.abs(ptrace))**2
return np.real((dim * (1 - L1) + psum) / (dim * (dim + 1)))
def qobj_to_rust_style(qobj, expect_state=False):
import qutip as qt
import numpy as np
data = None
n_qubits = 1
# Figure out what kind of qobj we have and convert accordingly.
if qobj.type == 'oper':
n_qubits = len(qobj.dims[0])
data = {
'Mixed' if expect_state else 'Unitary':
arr_to_rust_style(qobj.data.todense())
}
elif qobj.type == 'super':
n_qubits = len(qobj.dims[0][0])
data = {
'KrausDecomposition':
arr_to_rust_style(
np.array([op.data.todense() for op in qt.to_kraus(qobj)]))
}
return {"n_qubits": n_qubits, "data": data}