def product_pauli_z(q1, q2, coeff, n_q):
eye = np.eye(n_q)
return operators([[coeff, Pauli(eye[q1], np.zeros(n_q)) * Pauli(eye[q2], np.zeros(n_q))]])
def pauli_z(qubit, coeff, n_q):
eye = np.eye(n_q)
return operators([[coeff, Pauli(eye[qubit], np.zeros(n_q))]])
def pauli_i(coeff, n_q):
id_pauli = Pauli(np.zeros(n_q), np.zeros(n_q))
return operators([[coeff, id_pauli]])
def pauli_x(qubit, coeff, n_q):
eye = np.eye(n_q)
return operators([[coeff, Pauli(np.zeros(n_q), eye[qubit])]])
def get_tsp_qubitops(ins, penalty=1e5):
"""Generate Hamiltonian for TSP of a graph.
Args:
ins (TspData) : TSP data including coordinates and distances.
penalty (float) : Penalty coefficient for the constraints
Returns:
operator.Operator, float: operator for the Hamiltonian and a
constant shift for the obj function.
"""
num_nodes = ins.dim
num_qubits = num_nodes**2
zero = np.zeros(num_qubits, dtype=np.bool)
pauli_list = []
shift = 0
for i in range(num_nodes):
for j in range(num_nodes):
if i == j:
continue
for p in range(num_nodes):
q = (p + 1) % num_nodes
shift += ins.w[i, j] / 4
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
pauli_list.append([-ins.w[i, j] / 4, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[j * num_nodes + q] = True
pauli_list.append([-ins.w[i, j] / 4, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
zp[j * num_nodes + q] = True
pauli_list.append([ins.w[i, j] / 4, Pauli(zp, zero)])
for i in range(num_nodes):
for p in range(num_nodes):
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
pauli_list.append([penalty, Pauli(zp, zero)])
shift += -penalty
for p in range(num_nodes):
for i in range(num_nodes):
for j in range(i):
shift += penalty / 2
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
pauli_list.append([-penalty / 2, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[j * num_nodes + p] = True
pauli_list.append([-penalty / 2, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
zp[j * num_nodes + p] = True
pauli_list.append([penalty / 2, Pauli(zp, zero)])
for i in range(num_nodes):
for p in range(num_nodes):
for q in range(p):
shift += penalty / 2
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
pauli_list.append([-penalty / 2, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + q] = True
pauli_list.append([-penalty / 2, Pauli(zp, zero)])
zp = np.zeros(num_qubits, dtype=np.bool)
zp[i * num_nodes + p] = True
zp[i * num_nodes + q] = True
pauli_list.append([penalty / 2, Pauli(zp, zero)])
shift += 2 * penalty * num_nodes
return operators(paulis=pauli_list), shift