Create a bloq for galois multiplication (#1557)

This is the final PR in the series #1554, #1533, and #1516. These PRs implemented the GF($2^n$) multiplication construction from https://arxiv.org/abs/1910.02849v2 which has a toffoli complexity of $n^{\log_2{3}}$

Author: NoureldinYosri

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -578,6 +578,8 @@
             qualtran.bloqs.gf_arithmetic.gf2_multiplication._MULTIPLY_BY_CONSTANT_MOD_DOC,
             qualtran.bloqs.gf_arithmetic.gf2_multiplication._MULTIPLY_POLY_BY_ONE_PLUS_XK_DOC,
             qualtran.bloqs.gf_arithmetic.gf2_multiplication._BINARY_POLYNOMIAL_MULTIPLICATION_DOC,
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._GF2_SHIFT_RIGHT_MOD_DOC,
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._GF2_MUL_DOC,
         ],
     ),
     NotebookSpecV2(

qualtran/_infra/data_types.py

@@ -51,18 +51,16 @@
 import abc
 from enum import Enum
 from functools import cached_property
-from typing import Any, Iterable, List, Literal, Optional, Sequence, TYPE_CHECKING, Union
+from typing import Any, Iterable, List, Optional, Sequence, Union
 
 import attrs
+import galois
 import numpy as np
 from fxpmath import Fxp
 from numpy.typing import NDArray
 
 from qualtran.symbolics import bit_length, is_symbolic, SymbolicInt
 
-if TYPE_CHECKING:
-    import galois
-
 
 class QDType(metaclass=abc.ABCMeta):
     """This defines the abstract interface for quantum data types."""
@@ -870,6 +868,14 @@ def uint_to_montgomery(self, x: int) -> int:
         return (x * pow(2, int(self.bitsize), int(self.modulus))) % self.modulus
 
 
+def _poly_converter(p) -> Union[galois.Poly, None]:
+    if p is None:
+        return None
+    if isinstance(p, galois.Poly):
+        return p
+    return galois.Poly.Degrees(p)
+
+
 @attrs.frozen
 class QGF(QDType):
     r"""Galois Field type to represent elements of a finite field.
@@ -896,9 +902,7 @@ class QGF(QDType):
             The characteristic must be prime.
         degree: The degree $m$ of the field $GF(p^{m})$. The degree must be a positive integer.
         irreducible_poly: Optional galois.Poly instance that defines the field arithmetic.
-            This parameter is passed to `galois.GF(..., irreducible_poly=irreducible_poly)`.
-        element_repr: The string representation of the galois elements.
-            This parameter is passed to `galois.GF(..., repr=field_repr)`.
+            This parameter is passed to `galois.GF(..., irreducible_poly=irreducible_poly, verify=False)`.
 
     References
         [Finite Field](https://en.wikipedia.org/wiki/Finite_field)
@@ -910,8 +914,7 @@ class QGF(QDType):
 
     characteristic: SymbolicInt
     degree: SymbolicInt
-    irreducible_poly: Optional['galois.Poly'] = attrs.field()
-    element_repr: Literal["int", "poly", "power"] = attrs.field(default='int')
+    irreducible_poly: Optional['galois.Poly'] = attrs.field(converter=_poly_converter)
 
     @irreducible_poly.default
     def _irreducible_poly_default(self):
@@ -957,12 +960,13 @@ def gf_type(self):
             int(self.characteristic),
             int(self.degree),
             irreducible_poly=poly,
-            repr=self.element_repr,
+            verify=False,
+            repr='poly',
             compile='python-calculate',
         )
 
     def to_bits(self, x) -> List[int]:
-        """Yields individual bits corresponding to binary representation of x"""
+        """Returns individual bits corresponding to binary representation of x"""
         self.assert_valid_classical_val(x)
         return self._quint_equivalent.to_bits(int(x))
 

qualtran/bloqs/gf_arithmetic/__init__.py

@@ -17,8 +17,10 @@
 from qualtran.bloqs.gf_arithmetic.gf2_inverse import GF2Inverse
 from qualtran.bloqs.gf_arithmetic.gf2_multiplication import (
     BinaryPolynomialMultiplication,
+    GF2MulK,
     GF2Multiplication,
-    GF2MultiplyByConstantMod,
+    GF2MulViaKaratsuba,
+    GF2ShiftRight,
     MultiplyPolyByOnePlusXk,
 )
 from qualtran.bloqs.gf_arithmetic.gf2_square import GF2Square