netket.vqs.FullSumState

class netket.vqs.FullSumState

Bases: VariationalState

Variational State for a variational quantum state computed on the whole Hilbert space without Monte Carlo sampling by summing over the whole Hilbert space.

Expectation values and gradients are deterministic. The only non-deterministic part is due to the initialization seed used to generate the parameters.

Inheritance

__init__(hilbert, model=None, *, chunk_size=None, variables=None, init_fun=None, apply_fun=None, seed=None, mutable=False, training_kwargs={}, dtype=<class 'float'>)

Constructs the FullSumState.

Parameters:

• hilbert (AbstractHilbert) – The Hilbert space

• model – (Optional) The model. If not provided, you must provide init_fun and apply_fun.

• variables (Optional[Any]) – Optional dictionary for the initial values for the variables (parameters and model state) of the model.

• seed (Union[int, Any, None]) – rng seed used to generate a set of parameters (only if parameters is not passed). Defaults to a random one.

• mutable (Union[bool, str, Collection[str], DenyList]) – Name or list of names of mutable arguments. Use it to specify if the model has a state that can change during evaluation, but that should not be optimised. See also flax.linen.Module.apply() documentation (default=False)

• init_fun (Callable[[Any, Sequence[int], Any], Union[ndarray, Array]]) – Function of the signature f(model, shape, rng_key, dtype) -> Optional_state, parameters used to initialise the parameters. Defaults to the standard flax initialiser. Only specify if your network has a non-standard init method.

• apply_fun (Optional[Callable]) – Function of the signature f(model, variables, σ) that should evaluate the model. Defaults to model.apply(variables, σ). specify only if your network has a non-standard apply method.

• training_kwargs (dict) – a dict containing the optional keyword arguments to be passed to the apply_fun during training. Useful for example when you have a batchnorm layer that constructs the average/mean only during training.

• chunk_size (Optional[int]) – (Defaults to None) If specified, calculations are split into chunks where the neural network is evaluated at most on chunk_size samples at once. This does not change the mathematical results, but will trade a higher computational cost for lower memory cost.

Attributes

chunk_size

Suggested maximum size of the chunks used in forward and backward evaluations of the Neural Network model. If your inputs are smaller than the chunk size this setting is ignored.

This can be used to lower the memory required to run a computation with a very high number of samples or on a very large lattice. Notice that inputs and outputs must still fit in memory, but the intermediate computations will now require less memory.

This option comes at an increased computational cost. While this cost should be negligible for large-enough chunk sizes, don’t use it unless you are memory bound!

This option is an hint: only some operations support chunking. If you perform an operation that is not implemented with chunking support, it will fall back to no chunking. To check if this happened, set the environment variable NETKET_DEBUG=1.

hilbert

The descriptor of the Hilbert space on which this variational state is defined.

model

Returns the model definition of this variational state.

This field is optional, and is set to None if the variational state has been initialized using a custom function.

model_state: Optional[Any]

An Optional PyTree encoding a mutable state of the model that is not trained.

n_parameters

The total number of parameters in the model.

parameters

The pytree of the parameters of the model.

variables

The PyTree containing the parameters and state of the model, used when evaluating it.

Methods

expect(O)

Estimates the quantum expectation value for a given operator \(O\) or generic observable. In the case of a pure state \(\psi\) and an operator, this is \(\langle O\rangle= \langle \Psi|O|\Psi\rangle/\langle\Psi|\Psi\rangle\) otherwise for a mixed state \(\rho\), this is \(\langle O\rangle= \textrm{Tr}[\rho \hat{O}]/\textrm{Tr}[\rho]\).

Parameters:

O (AbstractOperator) – the operator or observable for which to compute the expectation value.

Return type:

Stats

Returns:

An estimation of the quantum expectation value \(\langle O\rangle\).

expect_and_forces(O, *, mutable=None)

Estimates the quantum expectation value and the corresponding force vector for a given operator O.

The force vector \(F_j\) is defined as the covariance of log-derivative of the trial wave function and the local estimators of the operator. For complex holomorphic states, this is equivalent to the expectation gradient \(\frac{\partial\langle O\rangle}{\partial(\theta_j)^\star} = F_j\). For real-parameter states, the gradient is given by \(\frac{\partial\partial_j\langle O\rangle}{\partial\partial_j\theta_j} = 2 \textrm{Re}[F_j]\).

Parameters:

• O (AbstractOperator) – The operator O for which expectation value and force are computed.

• mutable (Union[bool, str, Collection[str], DenyList, None]) – Can be bool, str, or list. Specifies which collections in the model_state should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. This is used to mutate the state of the model while you train it (for example to implement BatchNorm. Consult Flax’s Module.apply documentation for a more in-depth explanation).

Return type:

tuple[Stats, Any]

Returns:

An estimate of the quantum expectation value <O>. An estimate of the force vector \(F_j = \textrm{Cov}[\partial_j\log\psi, O_{\textrm{loc}}]\).

expect_and_grad(O, *, mutable=None, **kwargs)

Estimates the quantum expectation value and its gradient for a given operator \(O\).

Parameters:

• O (AbstractOperator) – The operator \(O\) for which expectation value and gradient are computed.

• mutable (Union[bool, str, Collection[str], DenyList, None]) –

  Can be bool, str, or list. Specifies which collections in the model_state should be treated as mutable: bool: all/no collections are mutable. str: The name of a single mutable collection. list: A list of names of mutable collections. This is used to mutate the state of the model while you train it (for example to implement BatchNorm. Consult Flax’s Module.apply documentation for a more in-depth explanation).

• use_covariance – whether to use the covariance formula, usually reserved for hermitian operators, \(\textrm{Cov}[\partial\log\psi, O_{\textrm{loc}}\rangle]\)

Return type:

tuple[Stats, Any]

Returns:

An estimate of the quantum expectation value <O>. An estimate of the gradient of the quantum expectation value <O>.

grad(Ô, *, use_covariance=None, mutable=None)

Estimates the gradient of the quantum expectation value of a given operator O.

Parameters:

• op (netket.operator.AbstractOperator) – the operator O.

• is_hermitian – optional override for whether to use or not the hermitian logic. By default it’s automatically detected.

• use_covariance (bool | None)

• mutable (bool | str | Collection[str] | DenyList | None)

Returns:

An estimation of the average gradient of the quantum expectation value <O>.

Return type:

array

init(seed=None, dtype=None)

Initialises the variational parameters of the variational state.

init_parameters(init_fun=None, *, seed=None)

Re-initializes all the parameters with the provided initialization function, defaulting to the normal distribution of standard deviation 0.01.

Warning

The init function will not change the dtype of the parameters, which is determined by the model. DO NOT SPECIFY IT INSIDE THE INIT FUNCTION

Parameters:

• init_fun (Optional[Callable[[Any, Sequence[int], Any], Union[ndarray, Array]]]) – a jax initializer such as jax.nn.initializers.normal(). Must be a Callable taking 3 inputs, the jax PRNG key, the shape and the dtype, and outputting an array with the valid dtype and shape. If left unspecified, defaults to jax.nn.initializers.normal(stddev=0.01)

• seed (Optional[Any]) – Optional seed to be used. The seed is synced across all MPI processes. If unspecified, uses a random seed.

log_value(σ)

Evaluate the variational state for a batch of states and returns the logarithm of the amplitude of the quantum state.

For pure states, this is \(\log(\langle\sigma|\psi\rangle)\), whereas for mixed states this is \(\log(\langle\sigma_r|\rho|\sigma_c\rangle)\), where \(\psi\) and \(\rho\) are respectively a pure state (wavefunction) and a mixed state (density matrix). For the density matrix, the left and right-acting states (row and column) are obtained as σr=σ[::,0:N] and σc=σ[::,N:].

Given a batch of inputs (Nb, N), returns a batch of outputs (Nb,).

Return type:

Array

Parameters:

σ (Array)

probability_distribution()

quantum_geometric_tensor(qgt_T=None)

Computes an estimate of the quantum geometric tensor G_ij. This function returns a linear operator that can be used to apply G_ij to a given vector or can be converted to a full matrix.

Parameters:

qgt_T (Optional[LinearOperator]) – the optional type of the quantum geometric tensor. By default it’s automatically selected.

Returns:

A linear operator representing the quantum geometric tensor.

Return type:

nk.optimizer.LinearOperator

reset()

Resets the sampled states. This method is called automatically every time that the parameters/state is updated.

to_array(normalize=True, allgather=True)

Returns the dense-vector representation of this state.

Parameters:

• normalize (bool) – If True, the vector is normalized to have L2-norm 1.

• allgather (bool)

Return type:

Array

Returns:

An exponentially large vector representing the state in the computational basis.

to_qobj()

Convert the variational state to a qutip’s ket Qobj.

Returns:

A qutip.Qobj object.