Use raw strings for docstrings

This silences `SyntaxWarning` in Python 3.12 that comes from the
MathJax math constructs inside the docstrings.

Author: mhucka

src/openfermion/linalg/erpa.py

@@ -11,7 +11,7 @@
 def erpa_eom_hamiltonian(
     h_ijkl: numpy.ndarray, tpdm: numpy.ndarray, p: int, q: int, r: int, s: int
 ) -> Union[float, complex]:
-    """
+    r"""
     Evaluate $\sum_{a,b,c,d}h_{a, b, d, c}<\psi[p^ q, [a^ b^ c d, r^ s]]\psi>$
 
     Args:

src/openfermion/linalg/wave_fitting.py

@@ -40,7 +40,7 @@ def fit_known_frequencies(
 
 
 def prony(signal: numpy.ndarray) -> Tuple[numpy.ndarray, numpy.ndarray]:
-    """Estimates amplitudes and phases of a sparse signal using Prony's method.
+    r"""Estimates amplitudes and phases of a sparse signal using Prony's method.
 
     Single-ancilla quantum phase estimation returns a signal
     $g(k)=\sum (aj*exp(i*k*phij))$, where aj and phij are the amplitudes

src/openfermion/linalg/wedge_product.py

@@ -67,7 +67,7 @@ def generate_parity_permutations(seq):
 
 
 def wedge(left_tensor, right_tensor, left_index_ranks, right_index_ranks):
-    """
+    r"""
     Implement the wedge product between left_tensor and right_tensor
 
     The wedge product is defined as

src/openfermion/utils/bch_expansion.py

@@ -16,7 +16,7 @@
 
 
 def bch_expand(*ops, **kwargs):
-    """Compute $\log[e^{x_1} ... e^{x_N}]$ using the BCH formula.
+    r"""Compute $\log[e^{x_1} ... e^{x_N}]$ using the BCH formula.
 
     This implementation is explained in arXiv:1712.01348.
 
@@ -65,7 +65,7 @@ def _bch_expand_multiple_terms(*ops, **kwargs):
 
 
 def _bch_expand_two_terms(x, y, order=6):
-    """Compute $\log[e^x e^y]$ using the Baker-Campbell-Hausdorff formula.
+    r"""Compute $\log[e^x e^y]$ using the Baker-Campbell-Hausdorff formula.
 
     Args:
         x: An operator for which multiplication and addition are supported.