quimb.operator.hilbertspace¶

Tools for defining and manipulating Hilbert spaces.

Classes¶

HilbertSpace

Take a set of 'sites' (any sequence of sortable, hashable objects), and

Functions¶

`parse_edges_to_unique`(edges)	Given a list of edges, return a sorted list of unique sites and edges.
`valid_z2_sector`(sector)	Check if the given sector is valid for Z2 symmetry.
`valid_u1_sector`(sector, nsites)	Check if the given sector is valid for U1 symmetry.
`valid_u1u1_sector`(sector, nsites)	Check if the given sector is valid for U1U1 symmetry.
`parse_symmetry_and_sector`(nsites[, sector, symmetry])
`parse_sites_dims`(sites, dims)	Parse a site and dimension specification.

Module Contents¶

quimb.operator.hilbertspace.parse_edges_to_unique(edges)[source]¶

Given a list of edges, return a sorted list of unique sites and edges.

Parameters:

edges (Iterable[tuple[hashable, hashable]]]) – The edges to parse.

Returns:

sites (list of hashable) – The unique sites in the edges, sorted.
edges (list of (hashable, hashable)) – The unique edges, sorted.

quimb.operator.hilbertspace.valid_z2_sector(sector)[source]¶: Check if the given sector is valid for Z2 symmetry.

quimb.operator.hilbertspace.valid_u1_sector(sector, nsites)[source]¶: Check if the given sector is valid for U1 symmetry.

quimb.operator.hilbertspace.valid_u1u1_sector(sector, nsites)[source]¶: Check if the given sector is valid for U1U1 symmetry.

quimb.operator.hilbertspace.parse_symmetry_and_sector(nsites, sector=None, symmetry=None)[source]¶

quimb.operator.hilbertspace.parse_sites_dims(sites, dims)[source]¶

Parse a site and dimension specification.

Parameters:

sites (int, sequence of hashable objects, or dict) – The sites to parse. If an integer, simply use range(sites). If a dict, the keys are the sites and the values are the dimensions.
dims (int or sequence of int) – The dimensions to parse. If an integer, all sites have the same dim.

Returns:

parsed_sites (list of hashable) – The parsed list of sites (as yet unsorted).
parsed_dims (dict[hashable, int]) – A dictionary mapping each site to its dimension.
dims_used (set[int]) – The set of unique dimensions used.

class quimb.operator.hilbertspace.HilbertSpace(sites, dims=2, order=None, sector=None, symmetry=None)[source]¶

Take a set of ‘sites’ (any sequence of sortable, hashable objects), and map this into a ‘register’ or linearly indexed range, optionally using a particular ordering. A symmetry and sector can also be specified, which will change the size of the Hilbert space and how the valid configurations are enumerated.

Some nomenclature:

site: a hashable label for a site in the Hilbert space. This can be any python object (e.g. tuple[str | int]).
register: a linear index for a site in the Hilbert space. This is an integer in the range [0, nsites), and requires an ordering of the sites.
configuration: a mapping from sites to their occupation number or spin state. This is a dictionary mapping from site to int.
flat configuration: a flat array of the occupation number or spin state of each site in the order given by this Hilbert space (i.e. a mapping of register to int). This is a 1D array of length nsites with dtype np.uint8, for efficient manipulation with numba and numpy.
rank: a linear index for a configuration in the Hilbert space, taking into account any symmetries and sectors. This is an integer in the range [0, size), where size is the size of the Hilbert space given the symmetry and sector.

Parameters:

sites (int, sequence of hashable objects, or dict) – The sites to map into a linear register. If an integer, simply use range(sites). If a dict, the keys are the sites and the values are the dimensions, in which case the dims argument is ignored.
dims (int or sequence of int, optional) – The local dimensions of each site. If an integer, all sites have the same dimension. If a sequence, it should be the same length as sites. You can also provide the dimensions as part of the sites argument by passing a dict, in which case this argument is ignored.
order (bool, sequence[hashable] or callable, optional) – How to order the sites. If None or False (default), the sites are kept in the order supplied. If True, the sites are sorted. If a sequence, it should be a permutation of the sites, and this will be used to order them. If a callable, it should be a sorting key function which will be used to order the sites.
sector ({None, str, int, ((int, int), (int, int))}, optional) – The sector of the Hilbert space. If None, no sector is assumed.
symmetry ({None, "Z2", "U1", "U1U1"}, optional) – The symmetry of the Hilbert space if any. If None and a sector is provided, the symmetry will be inferred from the sector if possible.

_size = None¶

_sizes = None¶

_strides = None¶

_pt = None¶

set_ordering(order)[source]¶

Set the ordering of the sites in this Hilbert space.

Parameters:: order (bool, sequence[hashable] or callable, optional) – How to order the sites. If None or False (default), the sites are kept in the order supplied. If True, the sites are sorted. If a sequence, it should be a permutation of the sites, and this will be used to order them. If a callable, it should be a sorting key function which will be used to order the sites.

classmethod from_edges(edges, order=None)[source]¶

Construct a HilbertSpace from a set of edges, which are pairs of sites.

Parameters:

edges (Iterable[tuple[hashable, hashable]]]) – The edges to parse.
order (bool, sequence[hashable] or callable, optional) – How to order the sites. If None or False (default), the sites are kept in the order supplied. If True, the sites are sorted. If a sequence, it should be a permutation of the sites, and this will be used to order them. If a callable, it should be a sorting key function which will be used to order the sites.

property sites¶: The ordered tuple of all sites in the Hilbert space.

property sector¶: The sector of the Hilbert space.

get_sector_numba(sector=None, symmetry=None)[source]¶

The sector of the Hilbert space, in ‘numba form’. A non-default symmetry and sector can be provided.

Parameters:

sector ({None, str, int, ((int, int), (int, int))}, optional) – The sector of the Hilbert space. If None, the default sector is used.
symmetry ({None, "Z2", "U1", "U1U1"}, optional) – The symmetry of the Hilbert space. If None, the default symmetry is used, or inferred from the supplied sector if possible.

Returns:

sector (ndarray[int64]) – The sector of the Hilbert space, in ‘numba form’. This is a 1D array of length 1, 2 or 4, depending on the symmetry.
symmetry (str) – The symmetry of the Hilbert space. This is one of “None”, “Z2”, “U1”, or “U1U1”.

property symmetry¶: The symmetry of the Hilbert space.

property nsites¶: The total number of sites in the Hilbert space.

get_sizes()[source]¶: Get a numpy array of the ordered sizes of each site in the Hilbert space.

property sizes¶: Get a numpy array of the ordered sizes of each site in the Hilbert space.

get_strides()[source]¶: Get the strides for each site in the Hilbert space.

property strides¶: Get the strides for each site in the Hilbert space.

get_pascal_table()[source]¶: Get a sufficiently large pascal table for this Hilbert space.

get_size(sector=None, symmetry=None)[source]¶

Get the size of the Hilbert space, optionally given a non-default symmetry and sector.

Parameters:

sector ({None, str, int, ((int, int), (int, int))}, optional) – The sector of the Hilbert space. If None, the default sector is used.
symmetry ({None, "Z2", "U1", "U1U1"}, optional) – The symmetry of the Hilbert space. If None, the default symmetry is used, or inferred from the supplied sector if possible.

property size¶: Get the size of this Hilbert space, taking into account the default symmetry and sector.

site_size(site)[source]¶: Get the local dimension of a given site.

site_to_reg(site)[source]¶: Convert a site to a linear register index.

reg_to_site(reg)[source]¶: Convert a linear register index back to a site.

has_site(site)[source]¶: Check if this HilbertSpace contains a given site.

rank_to_flatconfig(rank)[source]¶

Convert a rank (linear index) into a flat configuration.

Parameters:: rank (int) – The rank (linear index) to convert.
Returns:: flatconfig – A flat configuration, with the occupation number or spin state of each site in the order given by this HilbertSpace.
Return type:: ndarray[uint8]

flatconfig_to_rank(flatconfig)[source]¶

Convert a flat configuration into a rank (linear index).

Parameters:: flatconfig (ndarray[uint8]) – A flat configuration, with the occupation number or spin state of each site in the order given by this HilbertSpace.
Returns:: rank – The rank (linear index) of the flat configuration in the Hilbert space.
Return type:: int

config_to_flatconfig(config)[source]¶

Turn a configuration into a flat configuration, assuming the order given by this HilbertSpace.

Parameters:: config (dict[hashable, int]) – A dictionary mapping sites to their occupation number / spin.
Returns:: flatconfig – A flat configuration, with the occupation number or spin state of each site in the order given by this HilbertSpace.
Return type:: ndarray[uint8]

flatconfig_to_config(flatconfig)[source]¶

Turn a flat configuration into a configuration, assuming the order given by this HilbertSpace.

Parameters:: flatconfig (ndarray[uint8]) – A flat configuration, with the occupation number or spin state of each site in the order given by this HilbertSpace.
Returns:: config – A dictionary mapping sites to their occupation number / spin state.
Return type:: dict[hashable, int]

rank_to_config(rank)[source]¶

Convert a rank (linear index) into a configuration.

Parameters:: rank (int) – The rank (linear index) to convert.
Returns:: config – A dictionary mapping sites to their occupation number / spin state.
Return type:: dict[hashable, int]

config_to_rank(config)[source]¶

Convert a configuration into a rank (linear index).

Parameters:: config (dict[hashable, int]) – A dictionary mapping sites to their occupation number / spin state.
Returns:: rank – The rank (linear index) of the configuration in the Hilbert space.
Return type:: int

rand_rank(seed=None)[source]¶

Get a random rank (linear index) in the Hilbert space.

Parameters:: seed (None, int or numpy.random.Generator, optional) – The random seed or generator to use. If None, a new generator will be created with default settings.
Returns:: rank – A random rank in the Hilbert space.
Return type:: int64

rand_flatconfig(seed=None)[source]¶

Get a random flat configuration.

Parameters:: seed (None, int or numpy.random.Generator, optional) – The random seed or generator to use. If None, a new generator will be created with default settings.
Returns:: flatconfig – A flat configuration, with the occupation number or spin state of each site in the order given by this HilbertSpace.
Return type:: ndarray[uint8]

rand_config(seed=None)[source]¶

Get a random configuration.

Parameters:: seed (None, int or numpy.random.Generator, optional) – The random seed or generator to use. If None, a new generator will be created with default settings.
Returns:: config – A dictionary mapping sites to their occupation number / spin state.
Return type:: dict[hashable, np.uint8]

__repr__()[source]¶