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#
- is_finite#
- is_indexable#
Whether the space can be indexed with an integer
- local_size#
- local_states#
- n_states#
- shape#
- size#
- size_physical#
- Methods
- all_states()#
Returns all valid states of the Hilbert space.
Throws an exception if the space is not indexable.
- Return type:
- Returns:
A (n_states x size) batch of states. this corresponds to the pre-allocated array if it was passed.
- numbers_to_states(numbers)#
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.- Return type:
- ptrace(sites)#
Returns the hilbert space without the selected sites.
Not all hilbert spaces support this operation.
- 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:
- 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.]]
- 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()#
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.
- 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)#
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 (
ndarray
) – Batch of states to be converted into the corresponding integers.- Returns:
Array of integers corresponding to states.
- Return type:
numpy.darray