def test_rhf_params_to_matrix():
test_kappa = rhf_params_to_matrix(np.array([0.1, 0.2, 0.3, 0.4]), 4)
kappa = np.zeros((4, 4))
kappa[0, 2] = -0.1
kappa[0, 3] = -0.3
kappa[1, 2] = -0.2
kappa[1, 3] = -0.4
kappa -= kappa.T
assert np.allclose(test_kappa, kappa)
with pytest.raises(ValueError):
rhf_params_to_matrix(np.array([1.0 + 1j]), 2)
def test_fidelity():
parameters = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
u = sp.linalg.expm(rhf_params_to_matrix(parameters, 6))
opdm = np.array([[
0.766034130, -0.27166330, -0.30936072, -0.08471057, -0.04878244,
-0.01285432
],
[
-0.27166330, 0.67657015, -0.37519640, -0.02101843,
-0.03568214, -0.05034585
],
[
-0.30936072, -0.37519640, 0.55896791, 0.04267370,
-0.02258184, -0.08783738
],
[
-0.08471057, -0.02101843, 0.04267370, 0.05450848,
0.11291253, 0.17131658
],
[
-0.04878244, -0.03568214, -0.02258184, 0.11291253,
0.26821219, 0.42351185
],
[
-0.01285432, -0.05034585, -0.08783738, 0.17131658,
0.42351185, 0.67570713
]])
assert np.isclose(fidelity(u, opdm), 1.0)
opdm += 0.1
opdm = 0.5 * (opdm + opdm.T)
assert np.isclose(fidelity(u, opdm), 0.3532702370138279)
def test_fidelity_witness():
parameters = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9])
u = sp.linalg.expm(rhf_params_to_matrix(parameters, 6))
omega = [1] * 3 + [0] * 3
opdm = np.array([[0.766034130, -0.27166330, -0.30936072, -0.08471057, -0.04878244, -0.01285432],
[-0.27166330, 0.67657015, -0.37519640, -0.02101843, -0.03568214, -0.05034585],
[-0.30936072, -0.37519640, 0.55896791, 0.04267370, -0.02258184, -0.08783738],
[-0.08471057, -0.02101843, 0.04267370, 0.05450848, 0.11291253, 0.17131658],
[-0.04878244, -0.03568214, -0.02258184, 0.11291253, 0.26821219, 0.42351185],
[-0.01285432, -0.05034585, -0.08783738, 0.17131658, 0.42351185, 0.67570713]])
assert np.isclose(fidelity_witness(u, omega, opdm), 1.0)
opdm += 0.1
opdm = 0.5 * (opdm + opdm.T)
# higher than fidelity because of particle number breaking
assert np.isclose(fidelity_witness(u, omega, opdm), 0.7721525013371697)
def test_prepare_slater():
qubits = cirq.LineQubit.range(4)
kappa = rhf_params_to_matrix(np.array([0.1, 0.2, 0.3, 0.4]), 4)
u = sp.linalg.expm(kappa)
with pytest.raises(ValueError):
list(prepare_slater_determinant(qubits, u[:, :2].T, clean_ryxxy=5))
test_circuit = cirq.Circuit(prepare_slater_determinant(qubits, u[:, :2].T))
true_moments = [
cirq.Moment(operations=[
cirq.X.on(cirq.LineQubit(0)),
cirq.X.on(cirq.LineQubit(1)),
]),
cirq.Moment(operations=[
(cirq.ISWAP**0.5).on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.1676697243144354).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.1676697243144355).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
(cirq.ISWAP**0.5).on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(1)),
(cirq.ISWAP**0.5).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
(cirq.ISWAP**0.5).on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.rz(np.pi * 1.3947664179536838).on(cirq.LineQubit(2)),
cirq.rz(np.pi * -0.3947664179536837).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 0.795779308536894).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.20422069146310598).on(cirq.LineQubit(1)),
(cirq.ISWAP**0.5).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
(cirq.ISWAP**0.5).on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(0)),
(cirq.ISWAP**0.5).on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0212853739870422).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.02128537398704223).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
(cirq.ISWAP**0.5).on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(1)),
])
]
assert cirq.approx_eq(true_moments, test_circuit._moments, atol=1e-8)
test_circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :2].T, clean_ryxxy=2))
true_circuit = [
cirq.Moment(operations=[
cirq.X.on(cirq.LineQubit(0)),
cirq.X.on(cirq.LineQubit(1)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.1676697243144354).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.1676697243144355).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.rz(np.pi * 1.3947664179536838).on(cirq.LineQubit(2)),
cirq.rz(np.pi * -0.3947664179536837).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 0.795779308536894).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.20422069146310598).on(cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(0)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0212853739870422).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.02128537398704223).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0).on(cirq.LineQubit(1)),
])
]
assert cirq.approx_eq(true_circuit, test_circuit._moments, atol=1e-8)
test_circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :2].T, clean_ryxxy=3))
true_circuit = [
cirq.Moment(operations=[
cirq.X.on(cirq.LineQubit(0)),
cirq.X.on(cirq.LineQubit(1)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.1885030576477686).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.14683639098110218).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747
).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 0.8166126418702274).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.22505402479643932).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 1.4155997512870173).on(cirq.LineQubit(2)),
cirq.rz(np.pi * -0.3739330846203504).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747
).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(2)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0421187073203755).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.000452040653708897).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(2)),
])
]
assert cirq.approx_eq(true_circuit, test_circuit._moments, atol=1e-8)
test_circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :2].T, clean_ryxxy=4))
true_circuit = [
cirq.Moment(operations=[
cirq.X.on(cirq.LineQubit(0)),
cirq.X.on(cirq.LineQubit(1)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.1885030576477686).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.14683639098110218).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747
).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 0.8166126418702274).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.22505402479643932).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 1.4155997512870173).on(cirq.LineQubit(2)),
cirq.rz(np.pi * -0.3739330846203504).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(0), cirq.LineQubit(1)),
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747
).on(cirq.LineQubit(2), cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(0)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(2)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(3)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0421187073203755).on(cirq.LineQubit(1)),
cirq.rz(np.pi * -0.000452040653708897).on(cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.FSimGate(theta=-0.7853981633974483, phi=0.1308996938995747).
on(cirq.LineQubit(1), cirq.LineQubit(2)),
]),
cirq.Moment(operations=[
cirq.rz(np.pi * 1.0208333333333333).on(cirq.LineQubit(1)),
cirq.rz(np.pi * 0.020833333333333332).on(cirq.LineQubit(2)),
])
]
assert cirq.approx_eq(true_circuit, test_circuit._moments, atol=1e-8)
def unitary(params):
kappa = rhf_params_to_matrix(
params,
len(rhf_objective.occ) + len(rhf_objective.virt),
rhf_objective.occ, rhf_objective.virt)
return sp.linalg.expm(kappa)
def test_global_gradient_h4():
"""
Test the gradient at the solution given by psi4
"""
# first get molecule
rhf_objective, molecule, params, _, _ = make_h6_1_3()
# molecule = h4_linear_molecule(1.0)
nocc = molecule.n_electrons // 2
occ = list(range(nocc))
virt = list(range(nocc, molecule.n_orbitals))
qubits = cirq.LineQubit.range(molecule.n_orbitals)
u = sp.linalg.expm(
rhf_params_to_matrix(params, len(qubits), occ=occ, virt=virt))
circuit = cirq.Circuit(prepare_slater_determinant(qubits, u[:, :nocc].T))
simulator = cirq.Simulator(dtype=np.complex128)
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_alpha = get_opdm(wf, molecule.n_orbitals)
opdm = np.zeros((molecule.n_qubits, molecule.n_qubits),
dtype=np.complex128)
opdm[::2, ::2] = opdm_alpha
opdm[1::2, 1::2] = opdm_alpha
grad = rhf_objective.global_gradient_opdm(params, opdm_alpha)
# get finite difference gradient
finite_diff_grad = np.zeros(9)
epsilon = 0.0001
for i in range(9):
params_epsilon = params.copy()
params_epsilon[i] += epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
len(qubits),
occ=occ,
virt=virt))
circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :nocc].T))
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_pepsilon = get_opdm(wf, molecule.n_orbitals)
energy_plus_epsilon = rhf_objective.energy_from_opdm(opdm_pepsilon)
params_epsilon[i] -= 2 * epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
len(qubits),
occ=occ,
virt=virt))
circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :nocc].T))
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_pepsilon = get_opdm(wf, molecule.n_orbitals)
energy_minus_epsilon = rhf_objective.energy_from_opdm(opdm_pepsilon)
finite_diff_grad[i] = (energy_plus_epsilon -
energy_minus_epsilon) / (2 * epsilon)
assert np.allclose(finite_diff_grad, grad, atol=epsilon)
# random parameters now
params = np.random.randn(9)
u = sp.linalg.expm(
rhf_params_to_matrix(params, len(qubits), occ=occ, virt=virt))
circuit = cirq.Circuit(prepare_slater_determinant(qubits, u[:, :nocc].T))
simulator = cirq.Simulator(dtype=np.complex128)
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_alpha = get_opdm(wf, molecule.n_orbitals)
opdm = np.zeros((molecule.n_qubits, molecule.n_qubits),
dtype=np.complex128)
opdm[::2, ::2] = opdm_alpha
opdm[1::2, 1::2] = opdm_alpha
grad = rhf_objective.global_gradient_opdm(params, opdm_alpha)
# get finite difference gradient
finite_diff_grad = np.zeros(9)
epsilon = 0.0001
for i in range(9):
params_epsilon = params.copy()
params_epsilon[i] += epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
len(qubits),
occ=occ,
virt=virt))
circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :nocc].T))
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_pepsilon = get_opdm(wf, molecule.n_orbitals)
energy_plus_epsilon = rhf_objective.energy_from_opdm(opdm_pepsilon)
params_epsilon[i] -= 2 * epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
len(qubits),
occ=occ,
virt=virt))
circuit = cirq.Circuit(
prepare_slater_determinant(qubits, u[:, :nocc].T))
wf = simulator.simulate(circuit).final_state.reshape((-1, 1))
opdm_pepsilon = get_opdm(wf, molecule.n_orbitals)
energy_minus_epsilon = rhf_objective.energy_from_opdm(opdm_pepsilon)
finite_diff_grad[i] = (energy_plus_epsilon -
energy_minus_epsilon) / (2 * epsilon)
assert np.allclose(finite_diff_grad, grad, atol=epsilon)
def global_gradient_opdm(self, params: np.ndarray, alpha_opdm: np.ndarray):
opdm = np.zeros((self.num_qubits, self.num_qubits),
dtype=np.complex128)
opdm[::2, ::2] = alpha_opdm
opdm[1::2, 1::2] = alpha_opdm
tpdm = 2 * wedge(opdm, opdm, (1, 1), (1, 1))
# now go through and generate all the necessary Z, Y, Y_kl matrices
kappa_matrix = rhf_params_to_matrix(params,
len(self.occ) + len(self.virt),
self.occ, self.virt)
kappa_matrix_full = np.kron(kappa_matrix, np.eye(2))
w_full, v_full = np.linalg.eigh(
-1j * kappa_matrix_full) # so that kappa = i U lambda U^
eigs_scaled_full = get_matrix_of_eigs(w_full)
grad = np.zeros(self.nocc * self.nvirt, dtype=np.complex128)
kdelta = np.eye(self.num_qubits)
# NOW GENERATE ALL TERMS ASSOCIATED WITH THE GRADIENT!!!!!!
for p in range(self.nocc * self.nvirt):
grad_params = np.zeros_like(params)
grad_params[p] = 1
Y = rhf_params_to_matrix(grad_params,
len(self.occ) + len(self.virt), self.occ,
self.virt)
Y_full = np.kron(Y, np.eye(2))
# Now rotate Y int othe basis that diagonalizes Z
Y_kl_full = v_full.conj().T @ Y_full @ v_full
# now rotate Y_{kl} * (exp(i(l_{k} - l_{l})) - 1) / (i(l_{k} - l_{l}))
# into the original basis
pre_matrix_full = v_full @ (eigs_scaled_full *
Y_kl_full) @ v_full.conj().T
grad_expectation = -1.0 * np.einsum(
'ab,pq,aq,pb',
self.hamiltonian.one_body_tensor,
pre_matrix_full,
kdelta,
opdm,
optimize='optimal').real
grad_expectation += 1.0 * np.einsum(
'ab,pq,bp,aq',
self.hamiltonian.one_body_tensor,
pre_matrix_full,
kdelta,
opdm,
optimize='optimal').real
grad_expectation += 1.0 * np.einsum(
'ijkl,pq,iq,jpkl',
self.hamiltonian.two_body_tensor,
pre_matrix_full,
kdelta,
tpdm,
optimize='optimal').real
grad_expectation += -1.0 * np.einsum(
'ijkl,pq,jq,ipkl',
self.hamiltonian.two_body_tensor,
pre_matrix_full,
kdelta,
tpdm,
optimize='optimal').real
grad_expectation += -1.0 * np.einsum(
'ijkl,pq,kp,ijlq',
self.hamiltonian.two_body_tensor,
pre_matrix_full,
kdelta,
tpdm,
optimize='optimal').real
grad_expectation += 1.0 * np.einsum(
'ijkl,pq,lp,ijkq',
self.hamiltonian.two_body_tensor,
pre_matrix_full,
kdelta,
tpdm,
optimize='optimal').real
grad[p] = grad_expectation
return grad