netket.hilbert.DoubledHilbert

netket.hilbert.DoubledHilbert#

class netket.hilbert.DoubledHilbert[source]#

Bases: DoubledHilbert

Superoperatorial hilbert space for states living in the tensorised state \(\hat{H}\otimes \hat{H}\), encoded according to Choi’s isomorphism.

Inheritance

__init__(hilb)[source]#

Superoperatorial hilbert space for states living in the tensorised state \(\hat{H}\otimes \hat{H}\), encoded according to Choi’s isomorphism.

Parameters:: hilb (AbstractHilbert) – the Hilbert space H.

Examples

Simple superoperatorial hilbert space for few spins.

>>> import netket as nk
>>> g = nk.graph.Hypercube(length=5,n_dim=2,pbc=True)
>>> hi = nk.hilbert.Spin(N=3, s=0.5)
>>> hi2 = nk.hilbert.DoubledHilbert(hi)
>>> print(hi2.size)
6

Attributes

constrained#

The hilbert space does not contains prod(hilbert.shape) basis states.

Typical constraints are population constraints (such as fixed number of bosons, fixed magnetization…) which ensure that only a subset of the total unconstrained space is populated.

Typically, objects defined in the constrained space cannot be converted to QuTiP or other formats.

is_finite#: Whether the local hilbert space is finite.

is_indexable#: Whether the space can be indexed with an integer

local_size#: The local size of the Hilbert space, if defined on the Physical Hilbert space.

local_states#

Returns all valid states of the Hilbert space.

Throws an exception if the space is not indexable.

Returns:: A (n_states x size) batch of states. this corresponds to the pre-allocated array if it was passed.

n_states#: The total number of states in the Hilbert space. This should be the square of the number of states in the physical Hilbert space.

shape#: The size of the hilbert space on every site.

size#: The number number of degrees of freedom in the basis of this Hilbert space.

size_physical#: The size of the physical Hilbert space. In general this should be half of the size of the doubled Hilbert space.

Methods

all_states()[source]#

Returns all valid states of the Hilbert space.

Throws an exception if the space is not indexable.

Return type:: Union[ndarray, Array]
Returns:: A (n_states x size) batch of states. this corresponds to the pre-allocated array if it was passed.

numbers_to_states(numbers)[source]#

Returns the quantum numbers corresponding to the n-th basis state for input n.

n is an array of integer indices such that numbers[k]=Index(states[k]). Throws an exception iff the space is not indexable.

This function validates the inputs by checking that the numbers provided are smaller than the Hilbert space size, and throws an error if that condition is not met. When called from within a jax.jit context, this uses {func}`equinox.error_if` to throw runtime errors.

Parameters:: numbers (numpy.array) – Batch of input numbers to be converted into arrays of quantum numbers.
Return type:: Array

ptrace(sites)[source]#

Returns the hilbert space without the selected sites.

Not all hilbert spaces support this operation.

Parameters:: sites (int | Sequence[int]) – a site or list of sites to trace away
Return type:: Optional[Self]
Returns:: The partially-traced hilbert space. The type of the resulting hilbert space might be different from the starting one.

random_state(key=None, size=None, dtype=None)[source]#

Generates either a single or a batch of uniformly distributed random states. Runs as random_state(self, key, size=None, dtype=np.float32) by default.

Parameters:

key (Any) – rng state from a jax-style functional generator.
size (int | None) – If provided, returns a batch of configurations of the form (size, N) if size is an integer or (*size, N) if it is a tuple and where \(N\) is the Hilbert space size. By default, a single random configuration with shape (#,) is returned.
dtype – DType of the resulting vector.

Return type:

Array

Returns:

A state or batch of states sampled from the uniform distribution on the hilbert space.

Example

>>> import netket, jax
>>> hi = netket.hilbert.Qubit(N=2)
>>> k1, k2 = jax.random.split(jax.random.PRNGKey(1))
>>> print(hi.random_state(key=k1))
[0 0]
>>> print(hi.random_state(key=k2, size=2))
[[0 0]
 [0 0]]

size_at_index(i)[source]#

Size of the local degrees of freedom for the i-th variable.

Parameters:: i – The index of the desired site
Returns:: The number of degrees of freedom at that site

states()[source]#

Returns an iterator over all valid configurations of the Hilbert space. Throws an exception iff the space is not indexable. Iterating over all states with this method is typically inefficient, and `all_states` should be preferred.

Return type:: Iterator[ndarray]

states_at_index(i)[source]#

A list of discrete local quantum numbers at the site i. If the local states are infinitely many, None is returned.

Parameters:: i – The index of the desired site.
Returns:: A list of values or None if there are infinitely many.

states_to_local_indices(x)[source]#

Returns a tensor with the same shape of x, where all local values are converted to indices in the range 0…self.shape[i]. This function is guaranteed to be jax-jittable.

For the Fock space this returns x, but for other hilbert spaces such as Spin this returns an array of indices.

Warning

This function is experimental. Use at your own risk.

Parameters:: x – a tensor containing samples from this hilbert space
Returns:: a tensor containing integer indices into the local hilbert

states_to_numbers(states)[source]#

Returns the basis state number corresponding to given quantum states.

The states are given in a batch, such that states[k] has shape (hilbert.size). Throws an exception iff the space is not indexable.

Parameters:: states (Union[ndarray, Array]) – Batch of states to be converted into the corresponding integers.
Returns:: Array of integers corresponding to states.
Return type:: numpy.darray

netket.hilbert.DoubledHilbert

Contents

netket.hilbert.DoubledHilbert#