def trotter_step(
self,
qubits: Sequence[cirq.QubitId],
time: float,
control_qubit: Optional[cirq.QubitId] = None) -> cirq.OP_TREE:
n_qubits = len(qubits)
# Simulate the one-body terms for half of the full time
yield (rot11(rads=-0.5 * self.orbital_energies[i] * time).on(
control_qubit, qubits[i]) for i in range(n_qubits))
# Rotate to the computational basis
yield bogoliubov_transform(qubits, self.basis_change_matrix)
# Simulate the two-body terms for the full time
def two_body_interaction(p, q, a, b) -> cirq.OP_TREE:
yield rot111(-2 * self.hamiltonian.two_body[p, q] * time).on(
control_qubit, a, b)
yield swap_network(qubits, two_body_interaction)
# The qubit ordering has been reversed
qubits = qubits[::-1]
# Rotate back to the basis in which the one-body term is diagonal
yield cirq.inverse(
bogoliubov_transform(qubits, self.basis_change_matrix))
# Simulate the one-body terms for half of the full time
yield (rot11(rads=-0.5 * self.orbital_energies[i] * time).on(
control_qubit, qubits[i]) for i in range(n_qubits))
# Apply phase from constant term
yield cirq.Rz(rads=-self.hamiltonian.constant * time).on(control_qubit)
def trotter_step(
self,
qubits: Sequence[cirq.Qid],
time: float,
control_qubit: Optional[cirq.Qid]=None
) -> cirq.OP_TREE:
if not isinstance(control_qubit, cirq.Qid):
raise NotImplementedError('Control qudit must be specified.')
n_qubits = len(qubits)
# Change to the basis in which the one-body term is diagonal
yield bogoliubov_transform(
qubits, self.one_body_basis_change_matrix.T.conj())
# Simulate the one-body terms.
for p in range(n_qubits):
yield rot11(rads=
-self.one_body_energies[p] * time
).on(control_qubit, qubits[p])
# Simulate each singular vector of the two-body terms.
prior_basis_matrix = self.one_body_basis_change_matrix
for j in range(len(self.eigenvalues)):
# Get the two-body coefficients and basis change matrix.
two_body_coefficients = self.scaled_density_density_matrices[j]
basis_change_matrix = self.basis_change_matrices[j]
# Merge previous basis change matrix with the inverse of the
# current one
merged_basis_change_matrix = numpy.dot(prior_basis_matrix,
basis_change_matrix.T.conj())
yield bogoliubov_transform(qubits, merged_basis_change_matrix)
# Simulate the off-diagonal two-body terms.
yield swap_network(
qubits,
lambda p, q, a, b: rot111(
-2 * two_body_coefficients[p, q] * time).on(
control_qubit, a, b))
qubits = qubits[::-1]
# Simulate the diagonal two-body terms.
yield (rot11(rads=
-two_body_coefficients[k, k] * time).on(
control_qubit, qubits[k])
for k in range(n_qubits))
# Update prior basis change matrix.
prior_basis_matrix = basis_change_matrix
# Undo final basis transformation.
yield bogoliubov_transform(qubits, prior_basis_matrix)
# Apply phase from constant term
yield cirq.rz(rads=
-self.hamiltonian.constant * time).on(control_qubit)
def one_and_two_body_interaction_reverse_order(p, q, a,
b) -> cirq.OP_TREE:
yield rot11(rads=-self.hamiltonian.two_body[p, q] * time).on(a, b)
yield Ryxxy(0.5 * self.hamiltonian.one_body[p, q].imag * time).on(
a, b)
yield Rxxyy(0.5 * self.hamiltonian.one_body[p, q].real * time).on(
a, b)
def trotter_step(self,
qubits: Sequence[cirq.Qid],
time: float,
control_qubit: Optional[cirq.Qid] = None) -> cirq.OP_TREE:
n_qubits = len(qubits)
# Apply one- and two-body interactions for the full time
def one_and_two_body_interaction(p, q, a, b) -> cirq.OP_TREE:
yield CRxxyy(self.hamiltonian.one_body[p, q].real * time).on(
control_qubit, a, b)
yield CRyxxy(self.hamiltonian.one_body[p, q].imag * time).on(
control_qubit, a, b)
yield rot111(-2 * self.hamiltonian.two_body[p, q] * time).on(
control_qubit, a, b)
yield swap_network(qubits,
one_and_two_body_interaction,
fermionic=True)
qubits = qubits[::-1]
# Apply one-body potential for the full time
yield (rot11(rads=-self.hamiltonian.one_body[i, i].real * time).on(
control_qubit, qubits[i]) for i in range(n_qubits))
# Apply phase from constant term
yield cirq.rz(rads=-self.hamiltonian.constant * time).on(control_qubit)
def trotter_step(
self,
qubits: Sequence[cirq.Qid],
time: float,
control_qubit: Optional[cirq.Qid]=None
) -> cirq.OP_TREE:
n_qubits = len(qubits)
# Change to the basis in which the one-body term is diagonal
yield bogoliubov_transform(
qubits, self.one_body_basis_change_matrix.T.conj())
# Simulate the one-body terms.
for p in range(n_qubits):
yield cirq.Rz(rads=
-self.one_body_energies[p] * time
).on(qubits[p])
# Simulate each singular vector of the two-body terms.
prior_basis_matrix = self.one_body_basis_change_matrix
for j in range(len(self.eigenvalues)):
# Get the two-body coefficients and basis change matrix.
two_body_coefficients = self.scaled_density_density_matrices[j]
basis_change_matrix = self.basis_change_matrices[j]
# Merge previous basis change matrix with the inverse of the
# current one
merged_basis_change_matrix = numpy.dot(prior_basis_matrix,
basis_change_matrix.T.conj())
yield bogoliubov_transform(qubits, merged_basis_change_matrix)
# Simulate the off-diagonal two-body terms.
yield swap_network(
qubits,
lambda p, q, a, b: rot11(rads=
-2 * two_body_coefficients[p, q] * time).on(a, b))
qubits = qubits[::-1]
# Simulate the diagonal two-body terms.
for p in range(n_qubits):
yield cirq.Rz(rads=
-two_body_coefficients[p, p] * time
).on(qubits[p])
# Update prior basis change matrix
prior_basis_matrix = basis_change_matrix
# Undo final basis transformation
yield bogoliubov_transform(qubits, prior_basis_matrix)
def trotter_step(self,
qubits: Sequence[cirq.Qid],
time: float,
control_qubit: Optional[cirq.Qid] = None) -> cirq.OP_TREE:
n_qubits = len(qubits)
if not isinstance(control_qubit, cirq.Qid):
raise TypeError('Control qudit must be specified.')
# Apply one- and two-body interactions for half of the full time
def one_and_two_body_interaction(p, q, a, b) -> cirq.OP_TREE:
yield CRxxyy(0.5 * self.hamiltonian.one_body[p, q].real * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield CRyxxy(0.5 * self.hamiltonian.one_body[p, q].imag * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield rot111(-self.hamiltonian.two_body[p, q] * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield swap_network(qubits,
one_and_two_body_interaction,
fermionic=True)
qubits = qubits[::-1]
# Apply one-body potential for the full time
yield (rot11(rads=-self.hamiltonian.one_body[i, i].real * time).on(
control_qubit, qubits[i]) for i in range(n_qubits))
# Apply one- and two-body interactions for half of the full time
# This time, reorder the operations so that the entire Trotter step is
# symmetric
def one_and_two_body_interaction_reverse_order(p, q, a,
b) -> cirq.OP_TREE:
yield rot111(-self.hamiltonian.two_body[p, q] * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield CRyxxy(0.5 * self.hamiltonian.one_body[p, q].imag * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield CRxxyy(0.5 * self.hamiltonian.one_body[p, q].real * time).on(
cast(cirq.Qid, control_qubit), a, b)
yield swap_network(qubits,
one_and_two_body_interaction_reverse_order,
fermionic=True,
offset=True)
# Apply phase from constant term
yield cirq.rz(rads=-self.hamiltonian.constant * time).on(control_qubit)
def two_body_interaction(p, q, a, b) -> cirq.OP_TREE:
yield rot11(rads=-2 * self.hamiltonian.two_body[p, q] * time).on(
a, b)
