Add Unary mapping for bosonic operators (#6576)

**Context:**
Added Unary mapping

**Description of the Change:**
Added functions to map bosonic operators to qubit form using unary
mapping.

**Benefits:**

**Possible Drawbacks:**

**Related GitHub Issues:**
[sc-72640]

---------

Co-authored-by: Austin Huang <[email protected]>
Co-authored-by: Austin Huang <[email protected]>
Co-authored-by: soranjh <[email protected]>
Co-authored-by: Diego <[email protected]>

doc/code/qml_bose.rst

@@ -0,0 +1,32 @@
+qml.bose
+=========
+
+Overview
+--------
+
+This module contains functions and classes for creating and manipulating bosonic operators.
+
+
+BoseWord and BoseSentence
+---------------------------
+
+.. currentmodule:: pennylane.bose
+
+.. autosummary::
+    :toctree: api
+
+    ~BoseWord
+    ~BoseSentence
+
+Mapping to qubit operators
+--------------------------
+
+.. currentmodule:: pennylane.bose
+
+.. autosummary::
+    :toctree: api
+
+    ~binary_mapping
+    ~unary_mapping
+
+

doc/index.rst

@@ -193,6 +193,7 @@ PennyLane is **free** and **open source**, released under the Apache License, Ve
    :hidden:
 
    code/qml
+   code/qml_bose
    code/qml_compiler
    code/qml_data
    code/qml_debugging

doc/releases/changelog-dev.md

@@ -63,9 +63,13 @@
 * 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)
+
 * Added `binary_mapping()` function to map `BoseWord` and `BoseSentence` to qubit operators, using standard-binary mapping.
   [(#6564)](https://github.com/PennyLaneAI/pennylane/pull/6564)
 
+
 <h3>Improvements 🛠</h3>
 
 * Raises a comprehensive error when using `qml.fourier.qnode_spectrum` with standard numpy

pennylane/__init__.py

@@ -39,7 +39,12 @@
     parity_transform,
     bravyi_kitaev,
 )
-from pennylane.bose import BoseSentence, BoseWord, binary_mapping
+from pennylane.bose import (
+    BoseSentence,
+    BoseWord,
+    binary_mapping,
+    unary_mapping,
+)
 from pennylane.qchem import (
     taper,
     symmetry_generators,

pennylane/bose/__init__.py

@@ -14,4 +14,4 @@
 """A module containing utility functions and mappings for working with bosonic operators. """
 
 from .bosonic import BoseSentence, BoseWord
-from .bosonic_mapping import binary_mapping
+from .bosonic_mapping import unary_mapping, binary_mapping

pennylane/bose/bosonic_mapping.py

@@ -13,6 +13,7 @@
 # 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
 
@@ -159,3 +160,137 @@ def _(bose_operator: BoseSentence, n_states, tol=None):
     qubit_operator.simplify(tol=1e-16)
 
     return qubit_operator
+
+
+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:
+        Union[PauliSentence, Operator]: A linear combination of qubit operators.
+
+    **Example**
+
+    >>> w = qml.bose.BoseWord({(0, 0): "+"})
+    >>> 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})
+
+    ops_per_idx = defaultdict(list)
+
+    # Avoiding superfluous terms by taking the product of
+    # coefficient matrices.
+    for (_, b_idx), sign in bose_operator.items():
+        ops_per_idx[b_idx].append(sign)
+
+    for b_idx, signs in ops_per_idx.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