class netket.vqs.ExactState#

Bases: netket.vqs.VariationalState

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

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

Inheritance diagram of netket.vqs.ExactState
__init__(hilbert, model=None, *, variables=None, init_fun=None, apply_fun=None, seed=None, mutable=False, training_kwargs={}, dtype=<class 'float'>)[source]#

Constructs the ExactState.

  • hilbert (AbstractHilbert) – The Hilbert space

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

  • parameters – Optional PyTree of weights from which to start.

  • 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 (bool) – Dict specifing 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 (Optional[Callable[[Any, Sequence[int], Any], Union[ndarray, DeviceArray, Tracer]]]) – 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.

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

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

  • training_kwargs (Dict) – a dict containing the optionaal 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.


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

Return type



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.

Return type


model_state: Optional[Any]#

The optional pytree with the mutable state of the model.

Return type



The total number of parameters in the model.

Return type



The pytree of the parameters of the model.

Return type



The PyTreee containing the paramters and state of the model, used when evaluating it.

Return type


Estimates the quantum expectation value for a given operator O.

In the case of a pure state $psi$, this is $<O>= <Psi|O|Psi>/<Psi|Psi>$ otherwise for a mixed state $rho$, this is $<O> = Tr[rho hat{O}/Tr[rho]$.

Return type



An estimation of the quantum expectation value <O>.

expect_and_grad(Ô, *, mutable=None, use_covariance=None)#

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

  • – the operator Ô for which we compute the expectation value and its gradient

  • mutable (Optional[Any]) – 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 exaplanation).

  • use_covariance (Optional[bool]) – whever to use the covariance formula, usually reserved for hermitian operators, ⟨∂logψ Oˡᵒᶜ⟩ - ⟨∂logψ⟩⟨Oˡᵒᶜ⟩

  • Ô (netket.operator.AbstractOperator) –

Return type

Tuple[Stats, Any]


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


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

Return type


init(seed=None, dtype=None)[source]#

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.


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

  • init_fun (Optional[Callable[[Any, Sequence[int], Any], Union[ndarray, DeviceArray, Tracer]]]) – 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.


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 \(log(<σ|ψ>)\), whereas for mixed states this is \(log(<σr|ρ|σc>)\), where ψ and ρ 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



σ (jax._src.numpy.ndarray.ndarray) –


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.


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


A linear operator representing the quantum geometric tensor.

Return type



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

to_array(normalize=True, allgather=True)[source]#

Returns the dense-vector representation of this state.

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

  • allgather (bool) –

Return type



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


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


A qutip.Qobj object.