def make_XY_model(num_qubits):
import qubit_network.analytical_conditions as ac
def X(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i] = 1
return ac.pauli_product(*zeros)
def Y(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i] = 2
return ac.pauli_product(*zeros)
def Z(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i] = 3
return ac.pauli_product(*zeros)
def XX(i, j, num_qubits=3):
return X(i, num_qubits) * X(j, num_qubits)
def YY(i, j, num_qubits=3):
return Y(i, num_qubits) * Y(j, num_qubits)
expr = sympy.zeros(2**num_qubits, 2**num_qubits)
# all single-qubit interactions
for idx in range(num_qubits):
for pauli_idx in range(3):
mol = [0] * num_qubits
mol[idx] = pauli_idx + 1
expr += ac.pauli_product(*mol) * ac.J(*mol)
# only XX and YY two-qubit interactions
for pair in itertools.combinations(range(num_qubits), 2):
molXX = [0] * num_qubits
molXX[pair[0]] = 1
molXX[pair[1]] = 1
expr += ac.J(*molXX) * XX(pair[0], pair[1], num_qubits)
molYY = [0] * num_qubits
molYY[pair[0]] = 2
molYY[pair[1]] = 2
expr += ac.J(*molYY) * YY(pair[0], pair[1], num_qubits)
# return final expression
return expr
def make_XX_reduced_model():
import qubit_network.analytical_conditions as ac
def X(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 1
return ac.pauli_product(*zeros)
def Y(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 2
return ac.pauli_product(*zeros)
def Z(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 3
return ac.pauli_product(*zeros)
def XX(i, j, num_qubits=3):
first_term = X(i, num_qubits) * X(j, num_qubits)
second_term = Y(i, num_qubits) * Y(j, num_qubits)
return first_term + second_term
parametrized_hamiltonian = (ac.J(3, 0, 0) * Z(1) + ac.J(0, 1, 0) *
(X(2) + X(3)) + ac.J(0, 2, 0) * (Y(2) + Y(3)) +
ac.J(0, 3, 0) * (Z(2) + Z(3)) +
ac.J(0, 1, 1) * XX(2, 3) + ac.J(1, 1, 0) *
(XX(1, 2) + XX(1, 3)))
return parametrized_hamiltonian
def make_fredkin_model():
import qubit_network.analytical_conditions as ac
def X(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 1
return ac.pauli_product(*zeros)
def Y(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 2
return ac.pauli_product(*zeros)
def Z(i, num_qubits=3):
zeros = [0] * num_qubits
zeros[i - 1] = 3
return ac.pauli_product(*zeros)
def XY(i, j, num_qubits=3):
first_term = X(i, num_qubits) * X(j, num_qubits)
second_term = Y(i, num_qubits) * Y(j, num_qubits)
return first_term + second_term
num_qubits = 3
expr = sympy.zeros(2**num_qubits, 2**num_qubits)
# all single-qubit interactions
for idx in range(num_qubits):
for pauli_idx in range(3):
mol = [0] * num_qubits
mol[pauli_idx] = 1
expr += ac.pauli_product(*mol) * ac.J(*mol)
# only XY two-qubit interactions
for pair in itertools.combinations(range(num_qubits), 2):
expr += ac.J(pair[0], pair[1]) * XY(
pair[0], pair[1], num_qubits=num_qubits)
# return final expression
return expr
