def test_opt_basis_two_qubit_2d(self):
op = lib2.cnot()
# Classical input basis -> classical output basis
# Possible flip in control bit
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.subbasis([0, 1])
b_in = (b01, b0)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b01
assert op_c.bases_in[1] == b0
assert op_c.bases_out[0] == b01
assert op_c.bases_out[1] == b01
# Classical control bit is not violated
b = bases.general(2)
b0 = b.subbasis([0])
b_in = (b0, b)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b0
assert op_c.bases_in[1] == b
assert op_c.bases_out[0] == b0
assert op_c.bases_out[1] == b
# Classical target bit will become quantum for quantum control bit,
# input should not be violated
b = bases.general(2)
b0 = b.subbasis([0])
b_in = (b, b0)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b
assert op_c.bases_in[1] == b0
assert op_c.bases_out[0] == b
assert op_c.bases_out[1] == b
def test_opt_basis_two_qubit_2d(self):
op = lib2.cnot()
# Classical input basis -> classical output basis
# Possible flip in control bit
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.subbasis([0, 1])
b_in = (b01, b0)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b01
assert op_c.bases_in[1] == b0
assert op_c.bases_out[0] == b01
assert op_c.bases_out[1] == b01
# Classical control bit is not violated
b = bases.general(2)
b0 = b.subbasis([0])
b_in = (b0, b)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b0
assert op_c.bases_in[1] == b
assert op_c.bases_out[0] == b0
assert op_c.bases_out[1] == b
# Classical target bit will become quantum for quantum control bit,
# input should not be violated
b = bases.general(2)
b0 = b.subbasis([0])
b_in = (b, b0)
op_c = op.compile(bases_in=b_in)
assert op_c.bases_in[0] == b
assert op_c.bases_in[1] == b0
assert op_c.bases_out[0] == b
assert op_c.bases_out[1] == b
def test_chain_merge_prev(self, d, lib):
b = bases.general(d)
rng = np.random.RandomState(4242)
dm = rng.randn(d*d, d*d) + 1j * rng.randn(d*d, d*d)
dm += dm.conjugate().transpose()
dm /= dm.trace()
chain = Operation.from_sequence(
(lib.cphase(angle=np.pi/7, leakage=0.25)
if d == 3 else lib.cphase(3*np.pi / 7)).at(0, 1),
lib.rotate_x(4 * np.pi / 7).at(0),
)
bases_full = (b, b)
chain_c = chain.compile(bases_full, bases_full)
assert len(chain.operations) == 2
assert isinstance(chain_c, _PTMOperation)
state1 = State.from_dm(dm, bases_full)
state2 = State.from_dm(dm, bases_full)
chain(state1, 0, 1)
chain_c(state2, 0, 1)
assert np.allclose(state1.meas_prob(0), state2.meas_prob(0))
assert np.allclose(state1.meas_prob(1), state2.meas_prob(1))
def test_rotate_z(self):
sqrt2 = np.sqrt(2)
qubit_basis = (bases.general(2),)
dm = State(qubit_basis)
rotate90 = lib.rotate_z(0.5*np.pi)
rotate180 = lib.rotate_z(np.pi)
rotate360 = lib.rotate_z(2*np.pi)
rotate90(dm, 0)
assert np.allclose(dm.to_pv(), [1, 0, 0, 0])
rotate180(dm, 0)
assert np.allclose(dm.to_pv(), [1, 0, 0, 0])
# manually apply a Hadamard gate
had_expansion = np.array([0.5, 0.5, sqrt2, 0])
superpos_dm = State(qubit_basis,
had_expansion)
rotate180(superpos_dm, 0)
assert np.allclose(superpos_dm.to_pv(),
[0.5, 0.5, -sqrt2, 0])
rotate90(superpos_dm, 0)
assert np.allclose(superpos_dm.to_pv(),
[0.5, 0.5, 0, -sqrt2])
rotate180(superpos_dm, 0)
assert np.allclose(superpos_dm.to_pv(),
[0.5, 0.5, 0, sqrt2])
rotate360(superpos_dm, 0)
assert np.allclose(superpos_dm.to_pv(),
[0.5, 0.5, 0, sqrt2])
def test_chain_merge_prev(self, d, lib):
b = bases.general(d)
rng = np.random.RandomState(4242)
dm = rng.randn(d * d, d * d) + 1j * rng.randn(d * d, d * d)
dm += dm.conjugate().transpose()
dm /= dm.trace()
chain = Operation.from_sequence(
(lib.cphase(angle=np.pi / 7, leakage_rate=0.25)
if d == 3 else lib.cphase(3 * np.pi / 7)).at(0, 1),
lib.rotate_x(4 * np.pi / 7).at(0),
)
bases_full = (b, b)
chain_c = chain.compile(bases_full, bases_full)
assert len(chain._units) == 2
assert isinstance(chain_c, PTMOperation)
pv1 = PauliVector.from_dm(dm, bases_full)
pv2 = PauliVector.from_dm(dm, bases_full)
chain(pv1, 0, 1)
chain_c(pv2, 0, 1)
assert np.allclose(pv1.meas_prob(0), pv2.meas_prob(0))
assert np.allclose(pv1.meas_prob(1), pv2.meas_prob(1))
def meas_butterfly(p0_up, p1_up, p1_down, p2_down):
"""
Returns a gate, that corresponds to measurement-induced excitations.
Each measurement should be sandwiched by two of these gates (before
and after projection. This operation dephases the qubit immediately.
Note: if measurement-induced leakage is reported by RB, p1_up should
be twice larger, since RB would report average probabllity for both 0
and 1 state.
Parameters
----------
p0_up : float
Probability to excite to state 1, being in the state 0
p1_up : float
Probability to excite to state 2, being in the state 1
p1_down : float
Probability to relax to state 0, being in the state 1
p2_down : float
Probability to relax to state 1, being in the state 2
Returns
-------
quantumsim.operation._PTMOperation
"""
basis = (bases.general(3).computational_subbasis(), )
return amp_damping(0.5 * p0_up, 0.5 * p1_up, 0.5 * p1_down,
0.5 * p2_down).set_bases(bases_in=basis,
bases_out=basis)
def amp_damping(p0_up, p1_up, p1_down, p2_down):
"""
A gate, that excites or relaxes a qubit with a certain probability.
Parameters
----------
p0_up : float
Probability to excite to state 1, being in the state 0
p1_up : float
Probability to excite to state 2, being in the state 1
p1_down : float
Probability to relax to state 0, being in the state 1
p2_down : float
Probability to relax to state 1, being in the state 2
Returns
-------
quantumsim.operation._PTMOperation
"""
ptm = np.identity(9, dtype=float)
ptm[:3, :3] = [[1. - p0_up, p1_down, 0.],
[p0_up, 1. - p1_down - p1_up, p2_down],
[0., p1_up, 1 - p2_down]]
basis = (bases.general(3), )
return Operation.from_ptm(ptm, basis, basis)
def idle(duration, t1, t2, anharmonicity=0.):
if np.isfinite(t1) and np.isfinite(t2):
t_phi = 1. / (1. / t2 - 0.5 / t1)
if t_phi < 0:
raise ValueError('t2 must be less than 2*t1')
elif np.allclose(t_phi, 0):
ops_t2 = []
else:
ops_t2 = [(8. / (9 * t_phi))**0.5 *
np.array([[1, 0, 0], [0, 0, 0], [0, 0, -1]]),
(2. / (9 * t_phi))**0.5 *
np.array([[1, 0, 0], [0, -1, 0], [0, 0, 0]]),
(2. / (9 * t_phi))**0.5 *
np.array([[0, 0, 0], [0, 1, 0], [0, 0, -1]])]
else:
ops_t2 = []
op_t1 = t1**-0.5 * np.array([[0, 1, 0], [0, 0, np.sqrt(2)], [0, 0, 0]])
if not np.allclose(anharmonicity, 0.):
ham = np.array([
[0., 0., 0.],
[0., 0., 0.],
[0., 0., anharmonicity],
])
else:
ham = None
return Operation.from_lindblad_form(duration, (bases.general(3), ),
hamiltonian=ham,
lindblad_ops=[op_t1, *ops_t2])
def test_opt_basis_single_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b1 = b.subbasis([1])
b01 = b.computational_subbasis()
# Identity up to floating point error
rot = lib2.rotate_x(2 * np.pi).compile(bases_in=(b0,))
assert rot.bases_in == (b0,)
assert rot.bases_out == (b0,)
rot = lib2.rotate_x(2 * np.pi).compile(bases_in=(b1,))
assert rot.bases_in == (b1,)
assert rot.bases_out == (b1,)
# RX(pi)
rot = lib2.rotate_x(np.pi).compile(bases_in=(b0,))
assert rot.bases_in == (b0,)
assert rot.bases_out == (b1,)
rot = lib2.rotate_x(np.pi).compile(bases_in=(b1,))
assert rot.bases_in == (b1,)
assert rot.bases_out == (b0,)
# RY(pi/2)
rot = lib2.rotate_y(np.pi / 2).compile(bases_in=(b01,))
assert rot.bases_in[0] == b01
assert rot.bases_out[0].dim_pauli == 3
assert '0' in rot.bases_out[0].labels
assert '1' in rot.bases_out[0].labels
assert 'X10' in rot.bases_out[0].labels
def test_kraus_to_ptm_errors(self):
qubit_basis = (bases.general(2), )
qutrit_basis = (bases.general(3), )
cz_kraus_mat = np.diag([1, 1, 1, -1])
kraus_op = Operation.from_kraus(cz_kraus_mat, qubit_basis * 2)
wrong_dim_kraus = np.random.random((4, 4, 2, 2))
with pytest.raises(ValueError):
_ = Operation.from_kraus(wrong_dim_kraus, qubit_basis)
not_sqr_kraus = np.random.random((4, 2, 3))
with pytest.raises(ValueError):
_ = Operation.from_kraus(not_sqr_kraus, qubit_basis)
with pytest.raises(ValueError):
_ = Operation.from_kraus(cz_kraus_mat, qutrit_basis)
with pytest.raises(ValueError):
_ = kraus_op.set_bases(qutrit_basis * 2)
def test_lindblad_singlequbit(self):
ham = random_hermitian_matrix(2, seed=56)
lindblad_ops = np.array([
[[0, 0.1], [0, 0]],
[[0, 0], [0, 0.33]],
])
t1 = 10
t2 = 25
b1 = (bases.general(2), )
b2 = (bases.gell_mann(2), )
op1 = Operation.from_lindblad_form(t1,
b1,
b2,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op2 = Operation.from_lindblad_form(t2,
b2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op = Operation.from_lindblad_form(t1 + t2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
dm = random_hermitian_matrix(2, seed=3)
state1 = PauliVector.from_dm(dm, b1)
state2 = PauliVector.from_dm(dm, b1)
op1(state1, 0)
op2(state1, 0)
op(state2, 0)
assert np.allclose(state1.to_pv(), state2.to_pv())
def test_opt_basis_single_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b1 = b.subbasis([1])
b01 = b.computational_subbasis()
# Identity up to floating point error
rot = lib2.rotate_x(2 * np.pi).compile(bases_in=(b0, ))
assert rot.bases_in == (b0, )
assert rot.bases_out == (b0, )
rot = lib2.rotate_x(2 * np.pi).compile(bases_in=(b1, ))
assert rot.bases_in == (b1, )
assert rot.bases_out == (b1, )
# RX(pi)
rot = lib2.rotate_x(np.pi).compile(bases_in=(b0, ))
assert rot.bases_in == (b0, )
assert rot.bases_out == (b1, )
rot = lib2.rotate_x(np.pi).compile(bases_in=(b1, ))
assert rot.bases_in == (b1, )
assert rot.bases_out == (b0, )
# RY(pi/2)
rot = lib2.rotate_y(np.pi / 2).compile(bases_in=(b01, ))
assert rot.bases_in[0] == b01
assert rot.bases_out[0].dim_pauli == 3
assert '0' in rot.bases_out[0].labels
assert '1' in rot.bases_out[0].labels
assert 'X10' in rot.bases_out[0].labels
def test_chain_compile_leaking(self):
b = bases.general(3)
chain0 = Operation.from_sequence(
lib3.rotate_x(0.5 * np.pi).at(2),
lib3.cphase(leakage_rate=0.1).at(0, 2),
lib3.cphase(leakage_rate=0.1).at(1, 2),
lib3.rotate_x(-0.75 * np.pi).at(2),
lib3.rotate_x(0.25 * np.pi).at(2),
)
b0 = b.subbasis([0])
b01 = b.subbasis([0, 1])
b0134 = b.subbasis([0, 1, 3, 4])
chain1 = chain0.compile((b0, b0, b0134), (b, b, b))
assert isinstance(chain1, _Chain)
# Ancilla is not leaking here
anc_basis = chain1._units[1].operation.bases_out[1]
for label in anc_basis.labels:
assert '2' not in label
chain2 = chain0.compile((b01, b01, b0134), (b, b, b))
# Ancilla is leaking here
assert isinstance(chain2, _Chain)
anc_basis = chain2._units[1].operation.bases_out[1]
for label in '2', 'X20', 'Y20', 'X21', 'Y21':
assert label in anc_basis.labels
def test_create_untimed_model():
basis = (bases.general(2), )
class SampleModel(Model):
dim = 2
@Model.gate()
def rotate_y(self, qubit):
return (ParametrizedOperation(lib.rotate_y, basis), )
@Model.gate()
def cphase(self, qubit_static, qubit_fluxed):
return (lib.cphase(pi).at(qubit_static, qubit_fluxed), )
sample_setup = Setup("""
setup: []
""")
m = SampleModel(sample_setup)
cnot = m.rotate_y('D0', angle=0.5*pi) + m.cphase('D0', 'D1') + \
m.rotate_y('D0', angle=-0.5*pi)
assert cnot.finalize().operation.ptm(basis * 2, basis * 2) == approx(
Operation.from_sequence(
lib.rotate_y(0.5 * pi).at(0),
lib.cphase(pi).at(0, 1),
lib.rotate_y(-0.5 * pi).at(0),
).ptm(basis * 2, basis * 2))
def test_create_timed_model():
basis = (bases.general(2), )
class SampleModel(Model):
dim = 2
@Model.gate(duration=20)
def rotate_y(self, qubit):
return (
self.wait(qubit, 10),
ParametrizedOperation(lib.rotate_y, basis),
self.wait(qubit, 10),
)
@Model.gate(duration='t_twoqubit')
def cphase(self, qubit_static, qubit_fluxed):
return (
self.wait(qubit_static, 0.5 * self.p('t_twoqubit')),
self.wait(qubit_fluxed, 0.5 * self.p('t_twoqubit')),
lib.cphase(pi).at(qubit_static, qubit_fluxed),
self.wait(qubit_static, 0.5 * self.p('t_twoqubit')),
self.wait(qubit_fluxed, 0.5 * self.p('t_twoqubit')),
)
@Model.gate(duration=lambda qubit, setup: 600
if qubit == 'D0' else 400)
def strange_duration_gate(self, qubit):
return lib.rotate_y(pi)
@staticmethod
def _filter_wait_placeholders(operation):
return Operation.from_sequence([
unit for unit in operation.units()
if not isinstance(unit.operation, WaitPlaceholder)
])
def finalize(self, circuit, bases_in=None):
return circuit.finalize([self._filter_wait_placeholders], bases_in)
sample_setup = Setup("""
setup:
- t_twoqubit: 40
""")
m = SampleModel(sample_setup)
cnot = m.rotate_y('D0', angle=0.5*pi) + m.cphase('D0', 'D1') + \
m.rotate_y('D0', angle=-0.5*pi)
cnot = m.finalize(cnot)
assert cnot.operation.ptm(basis * 2, basis * 2) == approx(
Operation.from_sequence(
lib.rotate_y(0.5 * pi).at(0),
lib.cphase(pi).at(0, 1),
lib.rotate_y(-0.5 * pi).at(0),
).ptm(basis * 2, basis * 2))
gate1 = m.strange_duration_gate('D0')
assert gate1.duration == 600
gate2 = m.strange_duration_gate('D1')
assert gate2.duration == 400
def test_circuits_add(self):
dim = 2
orplus = lib.rotate_y(0.5 * pi)
ocphase = lib.cphase(pi)
orminus = lib.rotate_y(-0.5 * pi)
grplus = Gate('Q0', dim, orplus)
gcphase = Gate(('Q0', 'Q1'), dim, ocphase)
grminus = Gate('Q0', dim, orminus)
basis = (bases.general(2), ) * 2
circuit = grplus + gcphase
assert circuit.qubits == ['Q0', 'Q1']
assert len(circuit.gates) == 2
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0),
ocphase.at(0, 1)).ptm(basis, basis))
circuit = circuit + grminus
assert circuit.qubits == ['Q0', 'Q1']
assert len(circuit.gates) == 3
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0), ocphase.at(0, 1),
orminus.at(0)).ptm(basis, basis))
circuit = grplus + (gcphase + grminus)
assert circuit.qubits == ['Q0', 'Q1']
assert len(circuit.gates) == 3
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0), ocphase.at(0, 1),
orminus.at(0)).ptm(basis, basis))
grplus = Gate('Q1', dim, orplus)
grminus = Gate('Q1', dim, orminus)
circuit = grplus + gcphase + grminus
assert circuit.qubits == ['Q1', 'Q0']
assert len(circuit.gates) == 3
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0), ocphase.at(0, 1),
orminus.at(0)).ptm(basis, basis))
basis = (basis[0], ) * 3
grplus = Gate('Q2', dim, orplus)
grminus = Gate('Q0', dim, orminus)
circuit = grplus + gcphase + grminus
assert circuit.qubits == ['Q2', 'Q0', 'Q1']
assert len(circuit.gates) == 3
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0), ocphase.at(1, 2),
orminus.at(1)).ptm(basis, basis))
grplus = Gate('Q0', dim, orplus)
grminus = Gate('Q2', dim, orminus)
circuit = grplus + gcphase + grminus
assert circuit.qubits == ['Q0', 'Q1', 'Q2']
assert len(circuit.gates) == 3
assert c_op(circuit).ptm(basis, basis) == approx(
Operation.from_sequence(orplus.at(0), ocphase.at(0, 1),
orminus.at(2)).ptm(basis, basis))
def test_cnot(self):
cnot = lib.cnot()
qubit_bases = (bases.general(2), bases.general(2), bases.general(2))
dm = np.diag([0.25, 0, 0.75, 0, 0, 0, 0, 0])
s = PauliVector.from_dm(dm, qubit_bases)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (1, 0))
cnot(s, 0, 1)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (1, 0))
cnot(s, 1, 2)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (0.25, 0.75))
def test_lindblad_two_qubit(self):
b = (bases.general(2), )
id = np.array([[1, 0], [0, 1]])
ham1 = random_hermitian_matrix(2, seed=6)
ham2 = random_hermitian_matrix(2, seed=7)
ham = np.kron(ham1, id).reshape(2, 2, 2, 2) + \
np.kron(id, ham2).reshape(2, 2, 2, 2)
dm = random_hermitian_matrix(4, seed=3)
op1 = Operation.from_lindblad_form(25, b, hamiltonian=ham1)
op2 = Operation.from_lindblad_form(25, b, hamiltonian=ham2)
op = Operation.from_lindblad_form(25, b * 2, hamiltonian=ham)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
ops1 = np.array([
[[0, 0.1], [0, 0]],
[[0, 0], [0, 0.33]],
])
ops2 = np.array([
[[0, 0.15], [0, 0]],
[[0, 0], [0, 0.17]],
])
ops = [np.kron(op, id).reshape(2, 2, 2, 2) for op in ops1] +\
[np.kron(id, op).reshape(2, 2, 2, 2) for op in ops2]
op1 = Operation.from_lindblad_form(25, b, lindblad_ops=ops1)
op2 = Operation.from_lindblad_form(25, b, lindblad_ops=ops2)
op = Operation.from_lindblad_form(25, b * 2, lindblad_ops=ops)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
op1 = Operation.from_lindblad_form(25,
b,
hamiltonian=ham1,
lindblad_ops=ops1)
op2 = Operation.from_lindblad_form(25,
b,
hamiltonian=ham2,
lindblad_ops=ops2)
op = Operation.from_lindblad_form(25,
b * 2,
hamiltonian=ham,
lindblad_ops=ops)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
def test_lindblad_time_inverse(self):
ham = random_hermitian_matrix(2, seed=4)
b = (bases.general(2), )
op_plus = Operation.from_lindblad_form(20, b, hamiltonian=ham)
op_minus = Operation.from_lindblad_form(20, b, hamiltonian=-ham)
dm = random_hermitian_matrix(2, seed=5)
state = PauliVector.from_dm(dm, b)
op_plus(state, 0)
op_minus(state, 0)
assert np.allclose(state.to_dm(), dm)
def test_cnot(self):
cnot = lib.cnot()
qubit_bases = (bases.general(2),
bases.general(2),
bases.general(2))
dm = np.diag([0.25, 0, 0.75, 0, 0, 0, 0, 0])
s = State.from_dm(dm, qubit_bases)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (1, 0))
cnot(s, 0, 1)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (1, 0))
cnot(s, 1, 2)
assert np.allclose(s.meas_prob(0), (1, 0))
assert np.allclose(s.meas_prob(1), (0.25, 0.75))
assert np.allclose(s.meas_prob(2), (0.25, 0.75))
def test_compilation_with_placeholders(self):
b_full = bases.general(3)
b0 = b_full.subbasis([0])
b01 = b_full.subbasis([0, 1])
b012 = b_full.subbasis([0, 1, 2])
bases_in = (b01, b01, b0)
bases_out = (b_full, b_full, b012)
zz = Operation.from_sequence(
lib3.rotate_x(-np.pi / 2).at(2),
lib3.cphase(leakage_rate=0.1).at(0, 2),
lib3.cphase(leakage_rate=0.25).at(2, 1),
lib3.rotate_x(np.pi / 2).at(2),
lib3.rotate_x(np.pi).at(0),
lib3.rotate_x(np.pi).at(1)).compile(bases_in, bases_out)
ptm_ref = zz.ptm(bases_in, bases_out)
zz_parametrized = Operation.from_sequence(
Operation.from_sequence(
ParametrizedOperation(lambda angle1: lib3.rotate_x(angle1),
(b_full, )).at(2),
ParametrizedOperation(
lambda lr02: lib3.cphase(leakage_rate=lr02),
(b_full, ) * 2).at(0, 2),
ParametrizedOperation(
lambda lr21: lib3.cphase(leakage_rate=lr21),
(b_full, ) * 2).at(2, 1),
ParametrizedOperation(lambda angle2: lib3.rotate_x(angle2),
(b_full, )).at(2),
lib3.rotate_x(np.pi).at(0),
lib3.rotate_x(np.pi).at(1)))
zzpc = zz_parametrized.compile(bases_in, bases_out)
assert isinstance(zzpc, _Chain)
assert len(list(zzpc.units())) == 6
zz_parametrized = Operation.from_sequence(
Operation.from_sequence(
ParametrizedOperation(lambda angle1: lib3.rotate_x(angle1),
(b_full, )).at(2),
ParametrizedOperation(
lambda lr02: lib3.cphase(leakage_rate=lr02),
(b_full, ) * 2).at(0, 2),
lib3.cphase(leakage_rate=0.25).at(2, 1),
lib3.rotate_x(np.pi / 2).at(2),
lib3.rotate_x(np.pi).at(0),
lib3.rotate_x(np.pi).at(1)))
zzpc = zz_parametrized.compile(bases_in, bases_out)
assert len(list(zzpc.units())) == 4
params = dict(angle1=-np.pi / 2, lr02=0.1, foo='bar')
new_units = [(op.substitute(
**params) if isinstance(op, ParametrizedOperation) else op).at(*ix)
for op, ix in zzpc.units()]
zzpc = Operation.from_sequence(new_units).compile(bases_in, bases_out)
assert len(zzpc._units) == 2
assert zzpc.ptm(bases_in, bases_out) == approx(ptm_ref)
def test_rotate_euler(self):
qubit_basis = (bases.general(2),)
dm = State(qubit_basis + qubit_basis)
rotate90x = lib.rotate_euler(0, 0.5*np.pi, 0)
rotate90y = lib.rotate_euler(0, 0.5*np.pi, 0)
rotate90x(dm, 0)
assert np.allclose(dm.meas_prob(0), (0.5, 0.5))
rotate90y(dm, 1)
assert np.allclose(dm.meas_prob(1), (0.5, 0.5))
def test_compile_two_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.computational_subbasis()
op = lib2.cnot()
assert op.shape == (4, 4, 4, 4)
op_full = op.compile(bases_in=(b, b))
assert op_full.shape == (4, 4, 4, 4)
op_cl = op.compile(bases_in=(b01, b01))
assert op_cl.shape == (2, 2, 2, 2)
op_cl = op.compile(bases_in=(b0, b))
assert op_cl.shape == (1, 4, 1, 4)
def test_hadamard(self):
qubit_basis = (bases.general(2),)
sys_bases = qubit_basis+qubit_basis
dm = State(sys_bases)
hadamard = lib.hadamard()
hadamard(dm, 1)
assert np.allclose(dm.meas_prob(0), (1, 0))
assert np.allclose(dm.meas_prob(1), (0.5, 0.5))
hadamard(dm, 1)
assert np.allclose(dm.meas_prob(1), (1, 0))
def test_compile_two_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.computational_subbasis()
op = lib2.cnot()
assert op.shape == (4, 4, 4, 4)
op_full = op.compile(bases_in=(b, b))
assert op_full.shape == (4, 4, 4, 4)
op_cl = op.compile(bases_in=(b01, b01))
assert op_cl.shape == (2, 2, 2, 2)
op_cl = op.compile(bases_in=(b0, b))
assert op_cl.shape == (1, 4, 1, 4)
def test_convert_ptm_basis(self):
p_damp = 0.5
damp_kraus_mat = np.array([[[1, 0], [0, np.sqrt(1 - p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gell_mann_basis = (bases.gell_mann(2), )
general_basis = (bases.general(2), )
op1 = Operation.from_kraus(damp_kraus_mat, gell_mann_basis)
op2 = op1.set_bases(general_basis, general_basis) \
.set_bases(gell_mann_basis, gell_mann_basis)
assert np.allclose(op1.ptm(gell_mann_basis), op2.ptm(gell_mann_basis))
assert op1.bases_in == op2.bases_in
assert op1.bases_out == op2.bases_out
def test_convert_ptm_basis(self):
p_damp = 0.5
damp_kraus_mat = np.array(
[[[1, 0], [0, np.sqrt(1-p_damp)]],
[[0, np.sqrt(p_damp)], [0, 0]]])
gell_mann_basis = (bases.gell_mann(2),)
general_basis = (bases.general(2),)
damp_op_kraus = Operation.from_kraus(damp_kraus_mat, 2)
op1 = damp_op_kraus.set_bases(gell_mann_basis, gell_mann_basis)
op2 = damp_op_kraus.set_bases(general_basis, general_basis) \
.set_bases(gell_mann_basis, gell_mann_basis)
assert np.allclose(op1.ptm, op2.ptm)
assert op1.bases_in == op2.bases_in
assert op1.bases_out == op2.bases_out
def test_kraus_to_ptm_errors(self):
qutrit_basis = (bases.general(3),)
cz_kraus_mat = np.diag([1, 1, 1, -1])
kraus_op = Operation.from_kraus(cz_kraus_mat, 2)
wrong_dim_kraus = np.random.random((4, 4, 2, 2))
with pytest.raises(ValueError):
_ = Operation.from_kraus(wrong_dim_kraus, 2)
not_sqr_kraus = np.random.random((4, 2, 3))
with pytest.raises(ValueError):
_ = Operation.from_kraus(not_sqr_kraus, 2)
with pytest.raises(ValueError):
_ = Operation.from_kraus(cz_kraus_mat, 3)
with pytest.raises(ValueError):
_ = kraus_op.set_bases(qutrit_basis + qutrit_basis)
def test_create(self):
op_1q = lib2.rotate_x(0.5 * pi)
basis = (bases.general(2), )
with pytest.raises(ValueError,
match=".*can't accept free arguments.*"):
ParametrizedOperation(lambda *args: op_1q, basis, basis)
with pytest.raises(ValueError,
match=".*can't accept free keyword arguments.*"):
ParametrizedOperation(lambda **kwargs: op_1q, basis, basis)
with pytest.raises(OperationNotDefinedError,
match="Operation placeholder does not have a PTM"):
ParametrizedOperation(lambda: op_1q, basis).ptm(basis)
with pytest.raises(OperationNotDefinedError,
match="Operation placeholder can not be called"):
ParametrizedOperation(lambda: op_1q, basis)(PauliVector(basis))
def test_zz_parity_compilation(self):
b_full = bases.general(3)
b0 = b_full.subbasis([0])
b01 = b_full.subbasis([0, 1])
b012 = b_full.subbasis([0, 1, 2])
bases_in = (b01, b01, b0)
bases_out = (b_full, b_full, b012)
zz = Operation.from_sequence(
lib3.rotate_x(-np.pi / 2).at(2),
lib3.cphase(leakage_rate=0.1).at(0, 2),
lib3.cphase(leakage_rate=0.25).at(2, 1),
lib3.rotate_x(np.pi / 2).at(2),
lib3.rotate_x(np.pi).at(0),
lib3.rotate_x(np.pi).at(1))
zz_ptm = zz.ptm(bases_in, bases_out)
zzc = zz.compile(bases_in=bases_in, bases_out=bases_out)
zzc_ptm = zzc.ptm(bases_in, bases_out)
assert zz_ptm == approx(zzc_ptm)
units = list(zzc.units())
assert len(units) == 2
op1, ix1 = units[0]
op2, ix2 = units[1]
assert ix1 == (0, 2)
assert ix2 == (1, 2)
assert op1.bases_in[0] == bases_in[0]
assert op2.bases_in[0] == bases_in[1]
assert op1.bases_in[1] == bases_in[2]
# Qubit 0 did not leak
assert op1.bases_out[0] == bases_out[0].subbasis([0, 1])
# Qubit 1 leaked
assert op2.bases_out[0] == bases_out[1].subbasis([0, 1, 2, 6])
# Qubit 2 is measured
assert op2.bases_out[1] == bases_out[2]
dm = random_hermitian_matrix(3**3, seed=85)
pv1 = PauliVector.from_dm(dm, (b01, b01, b0))
pv2 = PauliVector.from_dm(dm, (b01, b01, b0))
zz(pv1, 0, 1, 2)
zzc(pv2, 0, 1, 2)
# Compiled version still needs to be projected, so we can't compare
# Pauli vectors, so we can to check only DM diagonals.
assert np.allclose(pv1.diagonal(), pv2.diagonal())
def test_circuits_params(self):
dim = 2
basis = (bases.general(dim), ) * 2
orotate = lib.rotate_y
ocphase = lib.cphase
grotate = Gate('Q0', dim, ParametrizedOperation(orotate, basis[:1]))
gcphase = Gate(('Q0', 'Q1'), dim,
ParametrizedOperation(ocphase, basis))
with pytest.raises(RuntimeError,
match=r".*free parameters.*\n"
r".*angle.*\n"
r".*allow_param_repeat.*"):
_ = gcphase + grotate
with allow_param_repeat():
circuit = grotate + gcphase + grotate
assert circuit.free_parameters == {sympy.symbols('angle')}
assert len(circuit.gates) == 3
angle = 0.736
assert c_op(circuit(angle=angle)).ptm(basis, basis) == \
approx(Operation.from_sequence(
orotate(angle).at(0), ocphase(angle).at(0, 1),
orotate(angle).at(0)
).ptm(basis, basis))
angle1 = 0.4 * pi
angle2 = 1.01 * pi
angle3 = -0.6 * pi
ptm_ref = Operation.from_sequence(
orotate(angle1).at(0),
ocphase(angle2).at(0, 1),
orotate(angle3).at(0)).ptm(basis, basis)
circuit = grotate(angle=angle1) + gcphase(angle=angle2) + \
grotate(angle=angle3)
assert circuit.finalize().operation.ptm(basis, basis) == \
approx(ptm_ref)
circuit = grotate(angle='angle1') + gcphase(angle='angle2') + \
grotate(angle='angle3')
assert c_op(circuit(angle1=angle1, angle2=angle2,
angle3=angle3)).ptm(basis,
basis) == approx(ptm_ref)
def test_zz_parity_compilation(self):
b_full = bases.general(3)
b0 = b_full.subbasis([0])
b01 = b_full.subbasis([0, 1])
b012 = b_full.subbasis([0, 1, 2])
bases_in = (b01, b01, b0)
bases_out = (b_full, b_full, b012)
zz = Operation.from_sequence(
lib3.rotate_x(-np.pi/2).at(2),
lib3.cphase(leakage=0.1).at(0, 2),
lib3.cphase(leakage=0.25).at(2, 1),
lib3.rotate_x(np.pi/2).at(2),
lib3.rotate_x(np.pi).at(0),
lib3.rotate_x(np.pi).at(1)
)
zzc = zz.compile(bases_in=bases_in, bases_out=bases_out)
assert len(zzc.operations) == 2
op1, ix1 = zzc.operations[0]
op2, ix2 = zzc.operations[1]
assert ix1 == (0, 2)
assert ix2 == (1, 2)
assert op1.bases_in[0] == bases_in[0]
assert op2.bases_in[0] == bases_in[1]
assert op1.bases_in[1] == bases_in[2]
# Qubit 0 did not leak
assert op1.bases_out[0] == bases_out[0].subbasis([0, 1, 3, 4])
# Qubit 1 leaked
assert op2.bases_out[0] == bases_out[1].subbasis([0, 1, 2, 6])
# Qubit 2 is measured
assert op2.bases_out[1] == bases_out[2]
dm = random_density_matrix(3**3, seed=85)
state1 = State.from_dm(dm, (b01, b01, b0))
state2 = State.from_dm(dm, (b01, b01, b0))
zz(state1, 0, 1, 2)
zzc(state2, 0, 1, 2)
# Compiled version still needs to be projected, so we can't compare
# Pauli vectors, so we can to check only DM diagonals.
assert np.allclose(state1.diagonal(), state2.diagonal())
def test_chain_apply(self):
b = (bases.general(2), ) * 3
dm = random_hermitian_matrix(8, seed=93)
pv1 = PauliVector.from_dm(dm, b)
pv2 = PauliVector.from_dm(dm, b)
# Some random gate sequence
op_indices = [(lib2.rotate_x(np.pi / 2), (0, )),
(lib2.rotate_y(0.3333), (1, )), (lib2.cphase(), (0, 2)),
(lib2.cphase(), (1, 2)),
(lib2.rotate_x(-np.pi / 2), (0, ))]
for op, indices in op_indices:
op(pv1, *indices),
circuit = Operation.from_sequence(*(op.at(*ix)
for op, ix in op_indices))
circuit(pv2, 0, 1, 2)
assert np.all(pv1.to_pv() == pv2.to_pv())
def test_compile_single_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.computational_subbasis()
op = lib2.rotate_y(np.pi)
assert op.shape == (4, 4)
op_full = op.compile(bases_in=(b,))
assert op_full.shape == (4, 4)
op_cl = op.compile(bases_in=(b01,))
assert op_cl.shape == (2, 2)
op = lib2.rotate_x(np.pi / 3)
assert op.shape == (4, 4)
op_full = op.compile(bases_in=(b,), bases_out=(b01,))
# X component of a state is irrelevant for the output.
assert op_full.shape == (2, 3)
op_cl = op.compile(bases_in=(b0,))
assert op_cl.shape == (3, 1)
def test_compile_single_qubit_2d(self):
b = bases.general(2)
b0 = b.subbasis([0])
b01 = b.computational_subbasis()
op = lib2.rotate_y(np.pi)
assert op.shape == (4, 4)
op_full = op.compile(bases_in=(b, ))
assert op_full.shape == (4, 4)
op_cl = op.compile(bases_in=(b01, ))
assert op_cl.shape == (2, 2)
op = lib2.rotate_x(np.pi / 3)
assert op.shape == (4, 4)
op_full = op.compile(bases_in=(b, ), bases_out=(b01, ))
# X component of a state is irrelevant for the output.
assert op_full.shape == (2, 3)
op_cl = op.compile(bases_in=(b0, ))
assert op_cl.shape == (3, 1)
def test_chain_compile_single_qubit(self, d, lib):
b = bases.general(d)
dm = random_hermitian_matrix(d, seed=487)
bases_full = (b, )
subbases = (b.subbasis([0, 1]), )
angle = np.pi / 5
rx_angle = lib.rotate_x(angle)
rx_2angle = lib.rotate_x(2 * angle)
chain0 = Operation.from_sequence(rx_angle.at(0), rx_angle.at(0))
pv0 = PauliVector.from_dm(dm, bases_full)
chain0(pv0, 0)
assert chain0.num_qubits == 1
assert len(chain0._units) == 2
chain0_c = chain0.compile(bases_full, bases_full)
assert isinstance(chain0_c, PTMOperation)
pv1 = PauliVector.from_dm(dm, bases_full)
chain0_c(pv1, 0)
assert chain0_c.num_qubits == 1
assert isinstance(chain0_c, PTMOperation)
op_angle = chain0_c
op_2angle = rx_2angle.compile(bases_full, bases_full)
assert isinstance(op_2angle, PTMOperation)
assert op_angle.shape == op_2angle.shape
assert op_angle.bases_in == op_2angle.bases_in
assert op_angle.bases_out == op_2angle.bases_out
assert op_angle.ptm(op_angle.bases_in, op_angle.bases_out) == \
approx(op_2angle.ptm(op_2angle.bases_in, op_2angle.bases_out))
assert pv1.to_pv() == approx(pv0.to_pv())
rx_pi = lib.rotate_x(np.pi)
chain_2pi = Operation.from_sequence(rx_pi.at(0), rx_pi.at(0))
chain_2pi_c1 = chain_2pi.compile(subbases, bases_full)
assert isinstance(chain_2pi_c1, PTMOperation)
assert chain_2pi_c1.bases_in == subbases
assert chain_2pi_c1.bases_out == subbases
chain_2pi_c2 = chain_2pi.compile(bases_full, subbases)
assert isinstance(chain_2pi_c2, PTMOperation)
assert chain_2pi_c2.bases_in == subbases
assert chain_2pi_c2.bases_out == subbases
def test_chain_compile_three_qubit(self, d, lib):
b = bases.general(d)
b0 = b.subbasis([0])
chain0 = Operation.from_sequence(
lib.rotate_x(0.5*np.pi).at(2),
lib.cphase().at(0, 2),
lib.cphase().at(1, 2),
lib.rotate_x(-0.75*np.pi).at(2),
lib.rotate_x(0.25*np.pi).at(2),
)
chain1 = chain0.compile((b, b, b0), (b, b, b))
assert chain1.operations[0].indices == (0, 2)
assert chain1.operations[0].operation.bases_in == (b, b0)
assert chain1.operations[0].operation.bases_out[0] == b
assert chain1.operations[1].indices == (1, 2)
assert chain1.operations[1].operation.bases_in[0] == b
assert chain1.operations[1].operation.bases_out[0] == b
for label in '0', '1', 'X10', 'Y10':
assert label in chain1.operations[1].operation.bases_out[1].labels
def test_chain_apply(self):
b = (bases.general(2), ) * 3
dm = random_density_matrix(8, seed=93)
state1 = State.from_dm(dm, b)
state2 = State.from_dm(dm, b)
# Some random gate sequence
op_indices = [(lib2.rotate_x(np.pi / 2), (0, )),
(lib2.rotate_y(0.3333), (1, )), (lib2.cphase(), (0, 2)),
(lib2.cphase(), (1, 2)),
(lib2.rotate_x(-np.pi / 2), (0, ))]
for op, indices in op_indices:
op(state1, *indices),
circuit = Operation.from_sequence(*(op.at(*ix)
for op, ix in op_indices))
circuit(state2, 0, 1, 2)
assert np.all(state1.to_pv() == state2.to_pv())
def test_chain_apply(self):
b = (bases.general(2),) * 3
dm = random_density_matrix(8, seed=93)
state1 = State.from_dm(dm, b)
state2 = State.from_dm(dm, b)
# Some random gate sequence
op_indices = [(lib2.rotate_x(np.pi/2), (0,)),
(lib2.rotate_y(0.3333), (1,)),
(lib2.cphase(), (0, 2)),
(lib2.cphase(), (1, 2)),
(lib2.rotate_x(-np.pi/2), (0,))]
for op, indices in op_indices:
op(state1, *indices),
circuit = Operation.from_sequence(
*(op.at(*ix) for op, ix in op_indices))
circuit(state2, 0, 1, 2)
assert np.all(state1.to_pv() == state2.to_pv())
def test_chain_compile_single_qubit(self, d, lib):
b = bases.general(d)
dm = random_density_matrix(d, seed=487)
bases_full = (b,)
subbases = (b.subbasis([0, 1]),)
angle = np.pi/5
rx_angle = lib.rotate_x(angle)
rx_2angle = lib.rotate_x(2*angle)
chain0 = Operation.from_sequence(rx_angle.at(0), rx_angle.at(0))
state0 = State.from_dm(dm, bases_full)
chain0(state0, 0)
assert chain0.num_qubits == 1
assert len(chain0.operations) == 2
chain0_c = chain0.compile(bases_full, bases_full)
state1 = State.from_dm(dm, bases_full)
chain0_c(state1, 0)
assert chain0_c.num_qubits == 1
assert isinstance(chain0_c, _PTMOperation)
op_angle = chain0_c
op_2angle = rx_2angle.compile(bases_full, bases_full)
assert op_angle.shape == op_2angle.shape
assert op_angle.bases_in == op_2angle.bases_in
assert op_angle.bases_out == op_2angle.bases_out
assert op_angle.ptm == approx(op_2angle.ptm)
assert state1.to_pv() == approx(state0.to_pv())
rx_pi = lib.rotate_x(np.pi)
chain_2pi = Operation.from_sequence(rx_pi.at(0), rx_pi.at(0))
chain_2pi_c1 = chain_2pi.compile(subbases, bases_full)
assert isinstance(chain_2pi_c1, _PTMOperation)
assert chain_2pi_c1.bases_in == subbases
assert chain_2pi_c1.bases_out == subbases
chain_2pi_c2 = chain_2pi.compile(bases_full, subbases)
assert isinstance(chain_2pi_c2, _PTMOperation)
assert chain_2pi_c2.bases_in == subbases
assert chain_2pi_c2.bases_out == subbases
def test_rotate_x(self):
basis = (bases.general(3),)
sys_bases = basis * 3
dm = State(sys_bases)
rotate90 = lib.rotate_x(0.5*np.pi)
rotate180 = lib.rotate_x(np.pi)
rotate360 = lib.rotate_x(2*np.pi)
rotate90(dm, 1)
rotate180(dm, 2)
assert np.allclose(dm.meas_prob(0), (1, 0, 0))
assert np.allclose(dm.meas_prob(1), (0.5, 0.5, 0))
assert np.allclose(dm.meas_prob(2), (0, 1, 0))
rotate180(dm, 1)
assert np.allclose(dm.meas_prob(1), (0.5, 0.5, 0))
rotate90(dm, 1)
assert np.allclose(dm.meas_prob(1), (1, 0, 0))
rotate360(dm, 0)
assert np.allclose(dm.meas_prob(0), (1, 0, 0))
def test_rotate_y(self):
qubit_basis = (bases.general(2),)
sys_bases = qubit_basis+qubit_basis+qubit_basis
dm = State(sys_bases)
rotate90 = lib.rotate_y(0.5*np.pi)
rotate180 = lib.rotate_y(np.pi)
rotate360 = lib.rotate_y(2*np.pi)
rotate90(dm, 1)
rotate180(dm, 2)
assert np.allclose(dm.meas_prob(0), (1, 0))
assert np.allclose(dm.meas_prob(1), (0.5, 0.5))
assert np.allclose(dm.meas_prob(2), (0, 1))
rotate180(dm, 1)
assert np.allclose(dm.meas_prob(1), (0.5, 0.5))
rotate90(dm, 1)
assert np.allclose(dm.meas_prob(1), (1, 0))
rotate360(dm, 0)
assert np.allclose(dm.meas_prob(0), (1, 0))
def test_chain_merge_next(self, d, lib):
b = bases.general(d)
dm = random_density_matrix(d**2, seed=574)
chain = Operation.from_sequence(
lib.rotate_x(np.pi / 5).at(0),
(lib.cphase(angle=3*np.pi/7, leakage=0.1)
if d == 3 else lib.cphase(3*np.pi / 7)).at(0, 1),
)
bases_full = (b, b)
chain_c = chain.compile(bases_full, bases_full)
assert len(chain.operations) == 2
assert isinstance(chain_c, _PTMOperation)
state1 = State.from_dm(dm, bases_full)
state2 = State.from_dm(dm, bases_full)
chain(state1, 0, 1)
chain_c(state2, 0, 1)
assert state1.meas_prob(0) == approx(state2.meas_prob(0))
assert state1.meas_prob(1) == approx(state2.meas_prob(1))
def test_chain_compile_leaking(self):
b = bases.general(3)
chain0 = Operation.from_sequence(
lib3.rotate_x(0.5*np.pi).at(2),
lib3.cphase(leakage=0.1).at(0, 2),
lib3.cphase(leakage=0.1).at(1, 2),
lib3.rotate_x(-0.75*np.pi).at(2),
lib3.rotate_x(0.25*np.pi).at(2),
)
b0 = b.subbasis([0])
b01 = b.subbasis([0, 1])
b0134 = b.subbasis([0, 1, 3, 4])
chain1 = chain0.compile((b0, b0, b0134), (b, b, b))
# Ancilla is not leaking here
anc_basis = chain1.operations[1].operation.bases_out[1]
for label in anc_basis.labels:
assert '2' not in label
chain2 = chain0.compile((b01, b01, b0134), (b, b, b))
# Ancilla is leaking here
anc_basis = chain2.operations[1].operation.bases_out[1]
for label in '2', 'X20', 'Y20', 'X21', 'Y21':
assert label in anc_basis.labels
def idle(duration, t1, t2, anharmonicity=0.):
t_phi = 1./(1./t2 - 0.5/t1)
op_t1 = t1**-0.5 * np.array([
[0, 1, 0],
[0, 0, np.sqrt(2)],
[0, 0, 0]
])
ops_t2 = [
(8. / (9*t_phi))**0.5 * np.array([
[1, 0, 0],
[0, 0, 0],
[0, 0, -1]
]),
(2. / (9*t_phi))**0.5 * np.array([
[1, 0, 0],
[0, -1, 0],
[0, 0, 0]
]),
(2. / (9*t_phi))**0.5 * np.array([
[0, 0, 0],
[0, 1, 0],
[0, 0, -1]
])
]
if not np.allclose(anharmonicity, 0.):
ham = np.array([
[0., 0., 0.],
[0., 0., 0.],
[0., 0., anharmonicity],
])
else:
ham = None
return Operation.from_lindblad_form(
duration, bases.general(3),
hamiltonian=ham,
lindblad_ops=[op_t1, *ops_t2])