# Copyright 2021 The NetKet Authors - All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Optional, Union
from netket.utils.types import DType
from netket.graph import AbstractGraph
from netket.hilbert import AbstractHilbert
from ._local_operator import LocalOperator
def check_acting_on_subspace(acting_on_subspace, hilbert, graph):
"""Check `acting_on_subspace` argument used by various operators."""
if acting_on_subspace is None:
acting_on_subspace = list(range(hilbert.size))
elif isinstance(acting_on_subspace, int):
start = acting_on_subspace
acting_on_subspace = [start + i for i in range(graph.n_nodes)]
elif isinstance(acting_on_subspace, list):
if len(acting_on_subspace) != graph.n_nodes:
raise ValueError(
"acting_on_subspace must be a list of length graph.n_nodes"
)
else:
raise TypeError("acting_on_subspace must be a list or single integer")
return acting_on_subspace
[docs]
class GraphOperator(LocalOperator):
r"""
A graph-based quantum operator. In its simplest terms, this is the sum of
local operators living on the edge of an arbitrary graph.
"""
[docs]
def __init__(
self,
hilbert: AbstractHilbert,
graph: AbstractGraph,
site_ops=[],
bond_ops=[],
bond_ops_colors=[],
dtype: Optional[DType] = None,
*,
acting_on_subspace: Union[None, list[int], int] = None,
):
r"""
A graph-based quantum operator. In its simplest terms, this is the sum of
local operators living on the edge of an arbitrary graph.
A ``GraphOperator`` is constructed giving a hilbert space and either a
list of operators acting on sites or a list acting on the bonds.
Users can specify the color of the bond that an operator acts on, if
desired. If none are specified, the bond operators act on all edges.
Args:
hilbert: Hilbert space the operator acts on.
graph: The graph whose vertices and edges are considered to construct the
operator
site_ops: A list of operators in matrix form that act
on the nodes of the graph.
The default is an empty list. Note that if no site_ops are
specified, the user must give a list of bond operators.
bond_ops: A list of operators that act on the edges of the graph.
The default is None. Note that if no bond_ops are
specified, the user must give a list of site operators.
bond_ops_colors: A list of edge colors, specifying the color each
bond operator acts on. The default is an empty list.
dtype: Data type of the matrix elements.
acting_on_subspace: Specifies the mapping between nodes of the graph and
Hilbert space sites, so that graph node :code:`i ∈ [0, ..., graph.n_nodes]`,
corresponds to :code:`acting_on_subspace[i] ∈ [0, ..., hilbert.n_sites]`.
Must be a list of length `graph.n_nodes`. Passing a single integer :code:`start`
is equivalent to :code:`[start, ..., start + graph.n_nodes - 1]`.
Examples:
Constructs a ``GraphOperator`` operator for a 2D system.
>>> import netket as nk
>>> sigmax = [[0, 1], [1, 0]]
>>> mszsz = [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, 1]]
>>> edges = [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8],
... [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15],
... [15, 16], [16, 17], [17, 18], [18, 19], [19, 0]]
>>> g = nk.graph.Graph(edges=edges)
>>> hi = nk.hilbert.Spin(0.5, N=g.n_nodes)
>>> op = nk.operator.GraphOperator(
... hi, site_ops=[sigmax], bond_ops=[mszsz], graph=g)
>>> print(op)
GraphOperator(dim=20, #acting_on=40 locations, constant=0.0, dtype=float64, graph=Graph(n_nodes=20, n_edges=20))
"""
acting_on_subspace = check_acting_on_subspace(
acting_on_subspace, hilbert, graph
)
self._acting_on_subspace = acting_on_subspace
# Ensure that at least one of SiteOps and BondOps was initialized
if len(bond_ops) == 0 and len(site_ops) == 0:
raise ValueError("Must input at least site_ops or bond_ops.")
# Create the local operator as the sum of all site and bond operators
operators = []
acting_on = []
# Site operators
if len(site_ops) > 0:
for i in range(graph.n_nodes):
for site_op in site_ops:
i_prime = acting_on_subspace[i]
operators.append(site_op)
acting_on.append([i_prime])
# Bond operators
if len(bond_ops_colors) > 0:
if len(bond_ops) != len(bond_ops_colors):
raise ValueError(
"""The GraphHamiltonian definition is inconsistent.
The sizes of bond_ops and bond_ops_colors do not match."""
)
if len(bond_ops) > 0:
# Use edge_colors to populate operators
for u, v, color in graph.edges(return_color=True):
u, v = acting_on_subspace[u], acting_on_subspace[v]
for c, bond_color in enumerate(bond_ops_colors):
if bond_color == color:
operators.append(bond_ops[c])
acting_on.append([u, v])
else:
assert len(bond_ops) == 1
for u, v in graph.edges():
u, v = acting_on_subspace[u], acting_on_subspace[v]
operators.append(bond_ops[0])
acting_on.append([u, v])
super().__init__(hilbert, operators, acting_on, dtype=dtype)
self._graph = graph
@property
def graph(self) -> AbstractGraph:
"""The graph on which this Operator is defined"""
return self._graph
@property
def acting_on_subspace(self):
"""
Mapping between nodes of the graph and Hilbert space sites as given in
the constructor.
"""
return self._acting_on_subspace
[docs]
def copy(self, *, dtype: Optional[DType] = None):
"""Returns a copy of the operator, while optionally changing the dtype
of the operator.
Args:
dtype: optional dtype
"""
return super().copy(dtype=dtype, _cls=LocalOperator)
def __repr__(self):
ao = self.acting_on
acting_str = f"acting_on={ao}"
if len(acting_str) > 55:
acting_str = f"#acting_on={len(ao)} locations"
return f"{type(self).__name__}(dim={self.hilbert.size}, {acting_str}, constant={self.constant}, dtype={self.dtype}, graph={self.graph})"
