# netket.hilbert.DoubledHilbert¶

class netket.hilbert.DoubledHilbert(hilb)

Bases: netket.hilbert.doubled_hilbert.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
is_finite
is_indexable

Whever the space can be indexed with an integer

Return type

bool

local_size
local_states
n_states
shape
size
size_physical
Methods
all_states(out=None)

Returns all valid states of the Hilbert space.

Throws an exception if the space is not indexable.

Parameters

out (Optional[ndarray]) – an optional pre-allocated output array

Return type

ndarray

Returns

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

numbers_to_states(numbers, out=None)

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.

Parameters
• numbers (numpy.array) – Batch of input numbers to be converted into arrays of quantum numbers.

• out (Optional[ndarray]) – Optional Array of quantum numbers corresponding to numbers.

Return type

ndarray

ptrace(sites)

Returns the hilbert space without the selected sites.

Not all hilbert spaces support this operation.

Parameters

sites (Union[int, Iterable]) – a site or list of sites to trace away

Return type

AbstractHilbert

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=<class 'numpy.float32'>)

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 – rng state from a jax-style functional generator.

• size (Optional[int]) – 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

ndarray

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))
[1. 0.]
>>> print(hi.random_state(key=k2, size=2))
[[0. 0.]
[0. 1.]]

states()

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 prefered.

Return type
states_to_numbers(states, out=None)

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
Returns

Array of integers corresponding to out.

Return type

numpy.darray