def evolve_fqe_givens_unrestricted(wfn: Wavefunction,
u: np.ndarray) -> Wavefunction:
"""Evolve a wavefunction by u generated from a 1-body Hamiltonian.
Args:
wfn: 2^{n} x 1 vector.
u: (n x n) unitary matrix.
Returns:
New evolved wfn object.
"""
rotations, diagonal = givens_decomposition_square(u.copy())
# Iterate through each layer and time evolve by the appropriate
# fermion operators
for layer in rotations:
for givens in layer:
i, j, theta, phi = givens
if not np.isclose(phi, 0):
op = of.FermionOperator(((j, 1), (j, 0)), coefficient=-phi)
wfn = wfn.time_evolve(1.0, op)
if not np.isclose(theta, 0):
op = of.FermionOperator(
((i, 1),
(j, 0)), coefficient=-1j * theta) + of.FermionOperator(
((j, 1), (i, 0)), coefficient=1j * theta)
wfn = wfn.time_evolve(1.0, op)
# evolve the last diagonal phases
for idx, final_phase in enumerate(diagonal):
if not np.isclose(final_phase, 1.0):
op = of.FermionOperator(((idx, 1), (idx, 0)),
-np.angle(final_phase))
wfn = wfn.time_evolve(1.0, op)
return wfn
def evolve_fqe_givens_sector(wfn: Wavefunction, u: np.ndarray,
sector='alpha') -> Wavefunction:
"""Evolve a wavefunction by u generated from a 1-body Hamiltonian.
Args:
wfn: FQE Wavefunction on n-orbitals
u: (n x n) unitary matrix.
sector: Optional either 'alpha' or 'beta' indicating which sector
to rotate
Returns:
New evolved wfn object.
"""
if sector == 'alpha':
sigma = 0
elif sector == 'beta':
sigma = 1
else:
raise ValueError("Bad section variable. Either (alpha) or (beta)")
if not np.isclose(u.shape[0], wfn.norb()):
raise ValueError(
"unitary is not specified for the correct number of orbitals")
rotations, diagonal = givens_decomposition_square(u.copy())
# Iterate through each layer and time evolve by the appropriate
# fermion operators
for layer in rotations:
for givens in layer:
i, j, theta, phi = givens
if not np.isclose(phi, 0):
op = of.FermionOperator(
((2 * j + sigma, 1), (2 * j + sigma, 0)), coefficient=-phi)
wfn = wfn.time_evolve(1.0, op)
if not np.isclose(theta, 0):
op = of.FermionOperator(((2 * i + sigma, 1),
(2 * j + sigma, 0)),
coefficient=-1j * theta) + \
of.FermionOperator(((2 * j + sigma, 1),
(2 * i + sigma, 0)),
coefficient=1j * theta)
wfn = wfn.time_evolve(1.0, op)
# evolve the last diagonal phases
for idx, final_phase in enumerate(diagonal):
if not np.isclose(final_phase, 1.0):
op = of.FermionOperator(
((2 * idx + sigma, 1), (2 * idx + sigma, 0)),
-np.angle(final_phase))
wfn = wfn.time_evolve(1.0, op)
return wfn
def evolve_fqe_charge_charge_sector(wfn: Wavefunction,
vij_mat: np.ndarray,
sector='alpha',
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j}v_{i, j}n_{i, alpha}n_{j, beta}}.`
Args:
wfn: fqe_wf with sdim = n
vij_mat: List[(n x n] matrices n is the spatial orbital rank
time: evolution time.
Returns:
New evolved 2^{2 * n} x 1 vector
"""
if sector == 'alpha':
sigma = 0
elif sector == 'beta':
sigma = 1
else:
raise ValueError("Sector must be alpha or beta.")
norbs = vij_mat.shape[0]
for p, q in product(range(norbs), repeat=2):
if np.isclose(vij_mat[p, q], 0):
continue
fop = of.FermionOperator(((2 * p + sigma, 1), (2 * p + sigma, 0),
(2 * q + sigma, 1), (2 * q + sigma, 0)),
coefficient=vij_mat[p, q])
wfn = wfn.time_evolve(time, fop)
return wfn
def test_evolve_spinful_fermionop(self):
"""
Make sure the spin-orbital reordering is working by comparing
time evolution
"""
wfn = Wavefunction([[2, 0, 2]])
wfn.set_wfn(strategy='random')
wfn.normalize()
cirq_wf = to_cirq(wfn).reshape((-1, 1))
op_to_apply = FermionOperator()
for p, q, r, s in product(range(2), repeat=4):
op = FermionOperator(
((2 * p, 1), (2 * q + 1, 1), (2 * r + 1, 0), (2 * s, 0)),
coefficient=numpy.random.randn())
op_to_apply += op + hermitian_conjugated(op)
opmat = get_sparse_operator(op_to_apply, n_qubits=4).toarray()
dt = 0.765
new_state_cirq = scipy.linalg.expm(-1j * dt * opmat) @ cirq_wf
new_state_wfn = from_cirq(new_state_cirq.flatten(), thresh=1.0E-12)
test_state = wfn.time_evolve(dt, op_to_apply)
self.assertTrue(
numpy.allclose(test_state.get_coeff((2, 0)),
new_state_wfn.get_coeff((2, 0))))
def evolve_fqe_diagaonal_coulomb(wfn: Wavefunction, vij_mat: np.ndarray,
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j, sigma, tau}v_{i, j}n_{i\sigma}n_{j\tau}}.`
Args:
wfn: 2^{n} x 1 vector.
vij_mat: List[(n//2 x n//2)] matrices
time: evolution time.
Returns:
New evolved 2^{n} x 1 vector
"""
dc_ham = DiagonalCoulomb(vij_mat)
return wfn.time_evolve(time, dc_ham)
def evolve_fqe_charge_charge_unrestricted(wfn: Wavefunction,
vij_mat: np.ndarray,
time=1) -> Wavefunction:
r"""Utility for testing evolution of a full 2^{n} wavefunction via
:math:`exp{-i time * \sum_{i,j}v_{i, j}n_{i}n_{j}}.`
Args:
wfn: fqe_wf with sdim = n
vij_mat: List[(n x n] matrices
time: evolution time.
Returns:
New evolved 2^{n} x 1 vector
"""
nso = vij_mat.shape[0]
for p, q in product(range(nso), repeat=2):
if np.isclose(vij_mat[p, q], 0):
continue
fop = of.FermionOperator(((p, 1), (p, 0), (q, 1), (q, 0)),
coefficient=vij_mat[p, q])
wfn = wfn.time_evolve(time, fop)
return wfn