def test_wrong_shape(self, hamiltonian):
"""Tests that an exception is raised if the Hamiltonian does not have
the correct shape"""
with pytest.raises(
ValueError, match="The Hamiltonian should have shape",
):
pu.decompose_hamiltonian(hamiltonian)
def test_decomposition(self, hamiltonian):
"""Tests that decompose_hamiltonian successfully decomposes Hamiltonians into a
linear combination of Pauli matrices"""
decomposed_coeff, decomposed_obs = pu.decompose_hamiltonian(hamiltonian)
linear_comb = sum([decomposed_coeff[i] * o.matrix for i, o in enumerate(decomposed_obs)])
assert np.allclose(hamiltonian, linear_comb)
def test_observable_types(self, hamiltonian, hide_identity):
"""Tests that the Hamiltonian decomposes into a linear combination of tensors,
the identity matrix, and Pauli matrices."""
allowed_obs = (Tensor, Identity, PauliX, PauliY, PauliZ)
decomposed_coeff, decomposed_obs = pu.decompose_hamiltonian(hamiltonian, hide_identity)
assert all([isinstance(o, allowed_obs) for o in decomposed_obs])
def test_result_length(self, hamiltonian):
"""Tests that tensors are composed of a number of terms equal to the number
of qubits."""
decomposed_coeff, decomposed_obs = pu.decompose_hamiltonian(hamiltonian)
n = int(np.log2(len(hamiltonian)))
tensors = filter(lambda obs: isinstance(obs, Tensor), decomposed_obs)
assert all(len(tensor.obs) == n for tensor in tensors)
def test_hide_identity_true(self):
"""Tests that there are no Identity observables in the tensor products
when hide_identity=True"""
H = np.array(np.diag([0, 0, 0, 1]))
coeff, obs_list = pu.decompose_hamiltonian(H, hide_identity=True)
tensors = filter(lambda obs: isinstance(obs, Tensor), obs_list)
for tensor in tensors:
all_identities = all(isinstance(o, Identity) for o in tensor.obs)
no_identities = not any(isinstance(o, Identity) for o in tensor.obs)
assert all_identities or no_identities
def test_decomp(self, H):
"""Tests that decompose_hamiltonian successfully decomposes Hamiltonians into Pauli matrices"""
N = int(np.log2(len(H)))
coeff, combs = pu.decompose_hamiltonian(H)
result = np.zeros((2**N, 2**N))
matrices = []
for term in combs:
base = [qml.Identity] * N
if term.num_wires == N:
matrices.append(term.matrix)
else:
base[term.wires[0]] = term.__class__
matrices.append(
functools.reduce(operator.matmul,
[t(i)
for i, t in enumerate(base)]).matrix)
for term in zip(coeff, matrices):
result = result + term[0] * term[1]
assert (H == result).all
def test_not_hermitian(self):
"""Tests that an exception is raised if the Hamiltonian is not Hermitian, i.e.
equal to its own conjugate transpose"""
with pytest.raises(ValueError,
match="The Hamiltonian is not Hermitian"):
pu.decompose_hamiltonian(np.array([[1, 2], [3, 4]]))
def find_excited_states(H):
"""
Fill in the missing parts between the # QHACK # markers below. Implement
a variational method that can find the three lowest energies of the provided
Hamiltonian.
Args:
H (qml.Hamiltonian): The input Hamiltonian
Returns:
The lowest three eigenenergies of the Hamiltonian as a comma-separated string,
sorted from smallest to largest.
"""
energies = np.zeros(3)
# QHACK #
w1 = range(len(H.wires))
w2 = range(len(H.wires))
dev = qml.device('default.qubit', wires=H.wires)
dev1 = qml.device('default.qubit', wires=w1)
dev2 = qml.device('default.qubit', wires=w2)
def variational_ansatz0(params, wires):
params = params[1:]
n_qubits = len(wires)
n_rotations = len(params)
if n_rotations > 1:
n_layers = n_rotations // n_qubits
n_extra_rots = n_rotations - n_layers * n_qubits
for layer_idx in range(n_layers):
layer_params = params[layer_idx * n_qubits : layer_idx * n_qubits + n_qubits, :]
qml.broadcast(qml.Rot, wires, pattern="single", parameters=layer_params)
qml.broadcast(qml.CNOT, wires, pattern="ring")
extra_params = params[-n_extra_rots:, :]
extra_wires = wires[: n_qubits - 1 - n_extra_rots : -1]
qml.broadcast(qml.Rot, extra_wires, pattern="single", parameters=extra_params)
else:
qml.Rot(*params[0], wires=wires[0])
def variational_ansatz1(params, wires):
rot_params = params[0]
params = params[1:]
n_qubits = len(wires)
n_rotations = len(params)
qml.PauliX(wires=0)
qml.RY(rot_params[1], wires=2)
if n_rotations > 1:
n_layers = n_rotations // n_qubits
n_extra_rots = n_rotations - n_layers * n_qubits
for layer_idx in range(n_layers):
layer_params = params[layer_idx * n_qubits : layer_idx * n_qubits + n_qubits, :]
qml.broadcast(qml.Rot, wires, pattern="single", parameters=layer_params)
qml.broadcast(qml.CNOT, wires, pattern="ring")
extra_params = params[-n_extra_rots:, :]
extra_wires = wires[: n_qubits - 1 - n_extra_rots : -1]
qml.broadcast(qml.Rot, extra_wires, pattern="single", parameters=extra_params)
else:
qml.Rot(*params[0], wires=wires[0])
@qml.qnode(dev1)
def get_state(params, wires=w2):
n_qubits = len(wires)
n_rotations = len(params)
if n_rotations > 1:
n_layers = n_rotations // n_qubits
n_extra_rots = n_rotations - n_layers * n_qubits
for layer_idx in range(n_layers):
layer_params = params[layer_idx * n_qubits : layer_idx * n_qubits + n_qubits, :]
qml.broadcast(qml.Rot, wires, pattern="single", parameters=layer_params)
qml.broadcast(qml.CNOT, wires, pattern="ring")
extra_params = params[-n_extra_rots:, :]
extra_wires = wires[: n_qubits - 1 - n_extra_rots : -1]
qml.broadcast(qml.Rot, extra_wires, pattern="single", parameters=extra_params)
else:
qml.Rot(*params[0], wires=wires[0])
return qml.state()
num_qubits = len(H.wires)
num_param_sets = (2 ** num_qubits) - 1
energy = 0
cost_fn = qml.ExpvalCost(variational_ansatz0, H, dev)
opt = qml.AdamOptimizer(stepsize=0.1)
params = np.random.normal(0, np.pi, (num_param_sets+1, 3))
conv_tol = 1e-08
max_iterations = 400
for n in range(max_iterations):
params, prev_energy = opt.step_and_cost(cost_fn, params)
energy = cost_fn(params)
conv = np.abs(energy - prev_energy)
if conv <= conv_tol:
break
energies[0] = energy
state_1 = get_state(params)
print(state_1)
additional_term = np.outer(state_1, state_1) * 3
coeffs, ops = decompose_hamiltonian(additional_term)
new_coeffs = (H.coeffs)
for c in coeffs:
new_coeffs.append(c)
new_ops = (H.ops)
for o in ops:
new_ops.append(o)
H1 = qml.Hamiltonian(new_coeffs, new_ops)
energy1 = 0
cost_fn_1 = qml.ExpvalCost(variational_ansatz, H1, dev)
params1 = np.random.normal(0, np.pi, (num_param_sets, 3))
for n in range(max_iterations):
params1, prev_energy = opt.step_and_cost(cost_fn_1, params1)
energy1 = cost_fn_1(params1)
conv = np.abs(energy1 - prev_energy)
if conv <= conv_tol:
break
energies[1] = energy1
# QHACK #
return ",".join([str(E) for E in energies])
def qubit_operator_string(self, observable):
"""Serializes a PennyLane observable to a string compatible with the
openfermion.QubitOperator class.
This method decomposes an observable into a sum of Pauli terms and
identities, if needed.
**Example**
>>> dev = QeQiskitDevice(wires=2)
>>> obs = qml.PauliZ(0)
>>> op_str = dev.qubit_operator_string(obs)
>>> print(op_str)
1 [Z0]
>>> obs = qml.Hadamard(0)
>>> op_str = dev.qubit_operator_string(obs)
>>> print(op_str)
0.7071067811865475 [X0] + 0.7071067811865475 [Z0]
Args:
observable (pennylane.operation.Observable): the observable to serialize
Returns:
str: the ``openfermion.QubitOperator`` string representation
"""
accepted_obs = {"PauliX", "PauliY", "PauliZ", "Identity"}
if isinstance(observable, Tensor):
need_decomposition = any(o.name not in accepted_obs
for o in observable.obs)
else:
need_decomposition = observable.name not in accepted_obs
if need_decomposition:
original_observable = observable
# Decompose the matrix of the observable
# This removes information about the wire labels used and
# consecutive integer wires are used
coeffs, obs_list = decompose_hamiltonian(
matrix(original_observable))
for idx in range(len(obs_list)):
obs = obs_list[idx]
if not isinstance(obs, Tensor):
# Convert terms to Tensor such that _terms_to_qubit_operator
# can be used
obs_list[idx] = Tensor(obs)
# Need to use the custom wire labels of the original observable
original_wires = original_observable.wires.tolist()
for o, mapped_w in zip(obs_list[idx].obs, original_wires):
o._wires = Wires(mapped_w)
else:
if not isinstance(observable, Tensor):
# If decomposition is not needed and is not a Tensor, we need
# to convert the single observable
observable = Tensor(observable)
coeffs = [1]
obs_list = [observable]
# Use consecutive integers as default wire_map
wire_map = {v: idx for idx, v in enumerate(self.wires)}
return _terms_to_qubit_operator_string(coeffs,
obs_list,
wires=wire_map)