from netket import legacy as nk # 1D Lattice g = nk.graph.Hypercube(length=20, n_dim=1, pbc=True) # Hilbert space of spins on the graph hi = nk.hilbert.Spin(s=1 / 2, N=g.n_nodes) # Ising spin hamiltonian ha = nk.operator.Ising(hilbert=hi, graph=g, h=1.0) # RBM Spin Machine # Paremeterizing phase and amplitude separately ma = nk.machine.RbmSpinPhase(alpha=1, hilbert=hi) ma.init_random_parameters(seed=1234, sigma=0.01) # Metropolis Local Sampling sa = nk.sampler.MetropolisLocal(machine=ma) # Optimizer op = nk.optimizer.Sgd(learning_rate=0.1) # Stochastic reconfiguration sr = nk.optimizer.SR(diag_shift=0.1) # ground-state optimization gs = nk.VMC(hamiltonian=ha, sampler=sa, optimizer=op, n_samples=1000, sr=sr) gs.run(n_iter=300, out="test")
# Hilbert space of spins on the graph
# with total Sz equal to 0
hi = nk.hilbert.Spin(s=1 / 2, N=g.n_nodes, total_sz=0)
# Heisenberg hamiltonian
ha = nk.operator.Heisenberg(hilbert=hi)
# Symmetric RBM Spin Machine
ma = nk.machine.JastrowSymm(hilbert=hi, automorphisms=g, dtype=float)
ma.init_random_parameters(seed=1234, sigma=0.01)
# Metropolis Exchange Sampling
# Notice that this sampler exchanges two neighboring sites
# thus preservers the total magnetization
sa = nk.sampler.MetropolisExchange(machine=ma)
# Optimizer
op = nk.optimizer.Sgd(ma, learning_rate=0.05)
# Stochastic reconfiguration
gs = nk.VMC(
hamiltonian=ha,
sampler=sa,
optimizer=op,
n_samples=1000,
sr=nk.optimizer.SR(diag_shift=0.1, lsq_solver="QR"),
)
gs.run(out="test", n_iter=300)
# Hilbert space of spins on the graph
hi = nk.hilbert.Spin(s=1 / 2) ** L
ha = nk.operator.Ising(hilbert=hi, graph=g, h=1.0)
alpha = 1
ma = nk.machine.JaxRbm(hi, alpha, dtype=float)
ma.init_random_parameters(seed=1232)
# Jax Sampler
sa = nk.sampler.MetropolisLocal(machine=ma, n_chains=32)
# Using Sgd
op = nk.optimizer.Sgd(ma, learning_rate=0.1)
# Create the optimization driver
gs = nk.VMC(
hamiltonian=ha,
sampler=sa,
optimizer=op,
n_samples=1000,
sr=None,
n_discard_per_chain=100,
)
# The first iteration is slower because of start-up jit times
gs.run(out="test", n_iter=2)
gs.run(out="test", n_iter=300)
# Custom Hamiltonian operator
ha = nk.operator.LocalOperator(hi)
for mat, site in zip(mats, sites):
ha += nk.operator.LocalOperator(hi, mat, site)
# Restricted Boltzmann Machine
ma = nk.machine.RbmSpin(hi, alpha=1, automorphisms=g)
ma.init_random_parameters(seed=1234, sigma=0.01)
# Exchange Sampler randomly exchange up to next-to-nearest neighbours
sa = nk.sampler.MetropolisExchange(machine=ma, n_chains=16, d_max=2)
# Optimizer
opt = nk.optimizer.Sgd(ma, learning_rate=0.02)
# Stochastic reconfiguration
sr = nk.optimizer.SR(ma, diag_shift=0.1)
# Variational Monte Carlo
gs = nk.VMC(
hamiltonian=op,
sampler=sa,
optimizer=opt,
sr=sr,
n_samples=4000,
n_discard_per_chain=5,
)
vmc.run(n_iter=300, out="test")
# Boson Hilbert Space
hi = nk.hilbert.Fock(N=g.n_nodes, n_max=3, n_bosons=8)
# Bose Hubbard Hamiltonian
ha = nk.operator.BoseHubbard(hilbert=hi, graph=g, U=4.0)
# RBM Machine with one-hot encoding, real parameters, and symmetries
ma = nk.machine.RbmMultiVal(hilbert=hi, alpha=1, dtype=float, automorphisms=g)
ma.init_random_parameters(seed=1234, sigma=0.01)
# Sampler using Hamiltonian moves, thus preserving the total number of particles
sa = nk.sampler.MetropolisHamiltonian(machine=ma,
hamiltonian=ha,
batch_size=16)
# Stochastic gradient descent optimization
op = nk.optimizer.Sgd(ma, 0.05)
# Variational Monte Carlo
sr = nk.optimizer.SR(ma, diag_shift=0.1)
vmc = nk.VMC(
hamiltonian=ha,
sampler=sa,
optimizer=op,
n_samples=4000,
n_discard_per_chain=0,
sr=sr,
)
vmc.run(n_iter=300, out="test")
# 1D Lattice
g = nk.graph.Hypercube(length=20, n_dim=1, pbc=True)
# Hilbert space of spins on the graph
hi = nk.hilbert.Spin(s=1 / 2, N=g.n_nodes)
# Ising spin hamiltonian
ha = nk.operator.Ising(hilbert=hi, graph=g, h=1.0)
# Jastrow Machine
ma = nk.machine.Jastrow(hilbert=hi)
ma.init_random_parameters(seed=1234, sigma=0.01)
# Metropolis Local Sampling
sa = nk.sampler.MetropolisLocal(machine=ma)
# Optimizer
op = nk.optimizer.Sgd(ma, learning_rate=0.1)
# Stochastic reconfiguration
gs = nk.VMC(
hamiltonian=ha,
sampler=sa,
optimizer=op,
n_samples=1000,
sr=nk.optimizer.SR(ma, diag_shift=0.1),
)
gs.run(n_iter=300, out="test")
