def test_autoregressive_sampling_with_lstm(self):
L = 4
# Set up symmetry orbit
orbit = jnp.array([
jnp.roll(jnp.identity(L, dtype=np.int32), l, axis=1)
for l in range(L)
])
# Set up variational wave function
rnn = nets.LSTM.partial(L=L, hiddenSize=5)
_, params = rnn.init_by_shape(random.PRNGKey(0), [(L, )])
rnnModel = nn.Model(rnn, params)
rbm = nets.RBM.partial(numHidden=2, bias=False)
_, params = rbm.init_by_shape(random.PRNGKey(0), [(L, )])
rbmModel = nn.Model(rbm, params)
psi = NQS((rnnModel, rbmModel))
# Set up exact sampler
exactSampler = sampler.ExactSampler(L)
# Set up MCMC sampler
mcSampler = sampler.MCMCSampler(random.PRNGKey(0),
jVMC.sampler.propose_spin_flip, (L, ),
numChains=777)
# Compute exact probabilities
_, logPsi, pex = exactSampler.sample(psi)
numSamples = 1000000
smc, p, _ = mcSampler.sample(psi, numSamples=numSamples)
self.assertTrue(jnp.max(jnp.abs(jnp.real(psi(smc) - p))) < 1e-12)
if global_defs.usePmap:
smc = smc.reshape((smc.shape[0] * smc.shape[1], -1))
self.assertTrue(smc.shape[0] >= numSamples)
# Compute histogram of sampled configurations
smcInt = jax.vmap(state_to_int)(smc)
pmc, _ = np.histogram(smcInt, bins=np.arange(0, 17))
self.assertTrue(
jnp.max(
jnp.abs(pmc / mcSampler.get_last_number_of_samples() -
pex.reshape((-1, ))[:16])) < 1e-3)
def test_MCMC_sampling(self):
L = 4
weights = jnp.array([
0.23898957, 0.12614753, 0.19479055, 0.17325271, 0.14619853,
0.21392751, 0.19648707, 0.17103704, -0.15457255, 0.10954413,
0.13228065, -0.14935214, -0.09963073, 0.17610707, 0.13386381,
-0.14836467
])
# Set up variational wave function
rbm = nets.CpxRBM.partial(numHidden=2, bias=False)
_, params = rbm.init_by_shape(random.PRNGKey(0), [(L, )])
rbmModel = nn.Model(rbm, params)
psi = NQS(rbmModel)
psi.set_parameters(weights)
# Set up exact sampler
exactSampler = sampler.ExactSampler(L)
# Set up MCMC sampler
mcSampler = sampler.MCMCSampler(random.PRNGKey(0),
jVMC.sampler.propose_spin_flip, (L, ),
numChains=777)
# Compute exact probabilities
_, _, pex = exactSampler.sample(psi)
# Get samples from MCMC sampler
numSamples = 500000
smc, _, _ = mcSampler.sample(psi, numSamples=numSamples)
if global_defs.usePmap:
smc = smc.reshape((smc.shape[0] * smc.shape[1], -1))
self.assertTrue(smc.shape[0] >= numSamples)
# Compute histogram of sampled configurations
smcInt = jax.vmap(state_to_int)(smc)
pmc, _ = np.histogram(smcInt, bins=np.arange(0, 17))
# Compare histogram to exact probabilities
self.assertTrue(
jnp.max(
jnp.abs(pmc / mcSampler.get_last_number_of_samples() -
pex.reshape((-1, ))[:16])) < 2e-3)
def test_gs_search_cpx(self):
L = 4
J = -1.0
hxs = [-1.3, -0.3]
exEs = [-6.10160339, -4.09296160]
for hx, exE in zip(hxs, exEs):
# Set up variational wave function
rbm = nets.CpxRBM.partial(numHidden=6, bias=False)
_, params = rbm.init_by_shape(random.PRNGKey(1), [(1, L)])
rbmModel = nn.Model(rbm, params)
psi = NQS(rbmModel)
# Set up hamiltonian for ground state search
hamiltonianGS = op.Operator()
for l in range(L):
hamiltonianGS.add(
op.scal_opstr(J, (op.Sz(l), op.Sz((l + 1) % L))))
hamiltonianGS.add(op.scal_opstr(hx, (op.Sx(l), )))
# Set up exact sampler
exactSampler = sampler.ExactSampler(L)
delta = 2
tdvpEquation = jVMC.tdvp.TDVP(exactSampler,
snrTol=1,
svdTol=1e-8,
rhsPrefactor=1.,
diagonalShift=delta,
makeReal='real')
# Perform ground state search to get initial state
ground_state_search(psi,
hamiltonianGS,
tdvpEquation,
exactSampler,
numSteps=100,
stepSize=2e-2)
obs = measure({"energy": hamiltonianGS}, psi, exactSampler)
self.assertTrue(
jnp.max(jnp.abs((obs['energy']['mean'] - exE) / exE)) < 1e-3)
def test_time_evolution(self):
L = 4
J = -1.0
hx = -0.3
weights = jnp.array([
0.23898957, 0.12614753, 0.19479055, 0.17325271, 0.14619853,
0.21392751, 0.19648707, 0.17103704, -0.15457255, 0.10954413,
0.13228065, -0.14935214, -0.09963073, 0.17610707, 0.13386381,
-0.14836467
])
# Set up variational wave function
rbm = nets.CpxRBM.partial(numHidden=2, bias=False)
_, params = rbm.init_by_shape(random.PRNGKey(0), [(1, L)])
rbmModel = nn.Model(rbm, params)
psi = NQS(rbmModel)
psi.set_parameters(weights)
# Set up hamiltonian for time evolution
hamiltonian = op.Operator()
for l in range(L):
hamiltonian.add(op.scal_opstr(J, (op.Sz(l), op.Sz((l + 1) % L))))
hamiltonian.add(op.scal_opstr(hx, (op.Sx(l), )))
# Set up ZZ observable
ZZ = op.Operator()
for l in range(L):
ZZ.add((op.Sz(l), op.Sz((l + 1) % L)))
# Set up exact sampler
exactSampler = sampler.ExactSampler(L)
# Set up adaptive time stepper
stepper = jVMCstepper.AdaptiveHeun(timeStep=1e-3, tol=1e-5)
tdvpEquation = jVMC.tdvp.TDVP(exactSampler,
snrTol=1,
svdTol=1e-8,
rhsPrefactor=1.j,
diagonalShift=0.,
makeReal='imag')
t = 0
obs = []
times = []
times.append(t)
newMeas = measure({'E': hamiltonian, 'ZZ': ZZ}, psi, exactSampler)
obs.append([newMeas['E']['mean'], newMeas['ZZ']['mean']])
while t < 0.5:
dp, dt = stepper.step(0,
tdvpEquation,
psi.get_parameters(),
hamiltonian=hamiltonian,
psi=psi,
numSamples=0)
psi.set_parameters(dp)
t += dt
times.append(t)
newMeas = measure({'E': hamiltonian, 'ZZ': ZZ}, psi, exactSampler)
obs.append([newMeas['E']['mean'], newMeas['ZZ']['mean']])
obs = np.array(jnp.asarray(obs))
# Check energy conservation
obs[:, 0] = np.abs((obs[:, 0] - obs[0, 0]) / obs[0, 0])
self.assertTrue(np.max(obs[:, 0]) < 1e-3)
# Check observable dynamics
zz = interp1d(np.array(times), obs[:, 1, 0])
refTimes = np.arange(0, 0.5, 0.05)
netZZ = zz(refTimes)
refZZ = np.array([
0.882762129306284, 0.8936168721790617, 0.9257753299594491,
0.9779836185039352, 1.0482156449061142, 1.1337654450614298,
1.231369697427413, 1.337354107391303, 1.447796176316155,
1.558696104640795, 1.666147269524912, 1.7664978782554912,
1.8564960156892512, 1.9334113379450693, 1.9951280521882777,
2.0402054805651546, 2.067904337137255, 2.078178742959828,
2.071635856483114, 2.049466698269522, 2.049466698269522
])
self.assertTrue(np.max(np.abs(netZZ - refZZ[:len(netZZ)])) < 1e-3)