Add Unary mapping for bosonic operators

doc/releases/changelog-dev.md

@@ -58,6 +58,9 @@
 * Added a second class `DefaultMixedNewAPI` to the `qml.devices.qubit_mixed` module, which is to be the replacement of legacy `DefaultMixed` which for now to hold the implementations of `preprocess` and `execute` methods.
   [(#6607)](https://github.com/PennyLaneAI/pennylane/pull/6507)
 
+* Added `unary_mapping()` function to map `BoseWord` and `BoseSentence` to qubit operators, using unary mapping.
+  [(#6576)](https://github.com/PennyLaneAI/pennylane/pull/6576)
+
 <h3>Improvements 🛠</h3>
 
 * Added support for the `wire_options` dictionary to customize wire line formatting in `qml.draw_mpl` circuit

pennylane/bose/__init__.py

@@ -1,3 +1,17 @@
+# Copyright 2018-2024 Xanadu Quantum Technologies Inc.
+
+# 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.
 """A module containing utility functions and mappings for working with bosonic operators. """
 
-from .bosonic import BoseWord, BoseSentence
+from .bosonic import BoseSentence, BoseWord
+from .bosonic_mapping import unary_mapping

pennylane/bose/bosonic_mapping.py

@@ -0,0 +1,172 @@
+# Copyright 2024 Xanadu Quantum Technologies Inc.
+
+# 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.
+"""This module contains functions to map bosonic operators to qubit operators."""
+
+from collections import defaultdict
+from functools import singledispatch
+from typing import Union
+
+import numpy as np
+
+import pennylane as qml
+from pennylane.pauli import PauliSentence, PauliWord
+
+from .bosonic import BoseSentence, BoseWord
+
+
+def _get_pauli_op(i, j, qub_id):
+    r"""Returns expression to convert qubit-local term ::math::``\ket{x_i}\bra{x_j}``
+    to qubit operators as given in :math:`Eq. (6-9)` in `arXiv.1909.12847 <https://arxiv.org/abs/1909.12847>`_.
+    """
+
+    c1, c2 = 0.5, -0.5 if i == 1 else 0.5
+
+    if i != j:
+        return PauliSentence({PauliWord({qub_id: "X"}): c1, PauliWord({qub_id: "Y"}): c2 * 1j})
+
+    return PauliSentence({PauliWord({}): c1, PauliWord({qub_id: "Z"}): c2})
+
+
+def unary_mapping(
+    bose_operator: Union[BoseWord, BoseSentence],
+    n_states: int = 2,
+    ps: bool = False,
+    wire_map: dict = None,
+    tol: float = None,
+):
+    r"""Convert a bosonic operator to a qubit operator using the unary mapping.
+
+    The mapping procedure is described in `arXiv.1909.12847 <https://arxiv.org/abs/1909.12847>`_.
+
+    Args:
+        bose_operator(BoseWord, BoseSentence): the bosonic operator
+        n_states(int): maximum number of allowed bosonic states
+        ps (bool): Whether to return the result as a PauliSentence instead of an
+            operator. Defaults to False.
+        wire_map (dict): A dictionary defining how to map the states of
+            the Bose operator to qubit wires. If None, integers used to
+            label the bosonic states will be used as wire labels. Defaults to None.
+        tol (float): tolerance for discarding the imaginary part of the coefficients
+
+    Returns:
+        a linear combination of qubit operators
+
+    **Example**
+
+    >>> w = qml.BoseWord()
+    >>> qml.unary_mapping(w, n_states=4)
+    0.25 * X(0) @ X(1)
+    + -0.25j * X(0) @ Y(1)
+    + 0.25j * Y(0) @ X(1)
+    + (0.25+0j) * Y(0) @ Y(1)
+    + 0.3535533905932738 * X(1) @ X(2)
+    + -0.3535533905932738j * X(1) @ Y(2)
+    + 0.3535533905932738j * Y(1) @ X(2)
+    + (0.3535533905932738+0j) * Y(1) @ Y(2)
+    + 0.4330127018922193 * X(2) @ X(3)
+    + -0.4330127018922193j * X(2) @ Y(3)
+    + 0.4330127018922193j * Y(2) @ X(3)
+    + (0.4330127018922193+0j) * Y(2) @ Y(3)
+    """
+
+    qubit_operator = _unary_mapping_dispatch(bose_operator, n_states, tol=tol)
+
+    wires = list(bose_operator.wires) or [0]
+    identity_wire = wires[0]
+    if not ps:
+        qubit_operator = qubit_operator.operation(wire_order=[identity_wire])
+
+    if wire_map:
+        return qubit_operator.map_wires(wire_map)
+
+    return qubit_operator
+
+
+@singledispatch
+def _unary_mapping_dispatch(bose_operator, n_states, ps=False, wires_map=None, tol=None):
+    """Dispatches to appropriate function if bose_operator is a BoseWord or BoseSentence."""
+    raise ValueError(f"bose_operator must be a BoseWord or BoseSentence, got: {bose_operator}")
+
+
+@_unary_mapping_dispatch.register
+def _(bose_operator: BoseWord, n_states, tol=None):
+
+    if n_states < 2:
+        raise ValueError(
+            f"Number of allowed bosonic states cannot be less than 2, provided {n_states}."
+        )
+
+    creation = np.zeros((n_states, n_states))
+    for i in range(n_states - 1):
+        creation[i + 1, i] = np.sqrt(i + 1.0)
+
+    coeff_mat = {"+": creation, "-": creation.T}
+
+    qubit_operator = PauliSentence({PauliWord({}): 1.0})
+
+    op_prod = defaultdict(list)
+
+    # Avoiding superfluous terms by taking the product of
+    # coefficient matrices.
+    for (_, b_idx), sign in bose_operator.items():
+        op_prod[b_idx].append(sign)
+
+    for b_idx, signs in op_prod.items():
+        coeff_mat_prod = np.eye(n_states)
+        for sign in signs:
+            coeff_mat_prod = np.dot(coeff_mat_prod, coeff_mat[sign])
+
+        op = PauliSentence()
+        sparse_coeffmat = np.nonzero(coeff_mat_prod)
+        for i, j in zip(*sparse_coeffmat):
+            coeff = coeff_mat_prod[i][j]
+
+            row = np.zeros(n_states)
+            row[i] = 1
+
+            col = np.zeros(n_states)
+            col[j] = 1
+
+            pauliOp = PauliSentence({PauliWord({}): 1.0})
+            for n in range(n_states):
+                if row[n] == 1 or col[n] == 1:
+                    pauliOp @= _get_pauli_op(row[n], col[n], n + b_idx * n_states)
+            op += coeff * pauliOp
+        qubit_operator @= op
+
+    for pw in qubit_operator:
+        if tol is not None and abs(qml.math.imag(qubit_operator[pw])) <= tol:
+            qubit_operator[pw] = qml.math.real(qubit_operator[pw])
+    qubit_operator.simplify(tol=1e-16)
+
+    return qubit_operator
+
+
+@_unary_mapping_dispatch.register
+def _(bose_operator: BoseSentence, n_states, tol=None):
+
+    qubit_operator = PauliSentence()
+
+    for bw, coeff in bose_operator.items():
+        bose_word_as_ps = unary_mapping(bw, n_states=n_states, ps=True)
+
+        for pw in bose_word_as_ps:
+            qubit_operator[pw] = qubit_operator[pw] + bose_word_as_ps[pw] * coeff
+
+            if tol is not None and abs(qml.math.imag(qubit_operator[pw])) <= tol:
+                qubit_operator[pw] = qml.math.real(qubit_operator[pw])
+
+    qubit_operator.simplify(tol=1e-16)
+
+    return qubit_operator

pennylane/qchem/__init__.py

@@ -82,3 +82,4 @@
     taper_hf,
     taper_operation,
 )
+