Add bloq for constant polynomial multiplication modulu in GF(2) (#1516)

* Fix bug in KaliskiStep3 and add tests for all steps

* cost

* Add bloq for constant polynomial multiplication modulu in GF(2)

* add notebook test

* nit

* mypy

* typo

* mypy

* typing

* fix all mypy

* fix typo

Author: NoureldinYosri

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -573,7 +573,10 @@
     NotebookSpecV2(
         title='GF($2^m$) Multiplication',
         module=qualtran.bloqs.gf_arithmetic.gf2_multiplication,
-        bloq_specs=[qualtran.bloqs.gf_arithmetic.gf2_multiplication._GF2_MULTIPLICATION_DOC],
+        bloq_specs=[
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._GF2_MULTIPLICATION_DOC,
+            qualtran.bloqs.gf_arithmetic.gf2_multiplication._MULTIPLY_BY_CONSTANT_MOD_DOC,
+        ],
     ),
     NotebookSpecV2(
         title='GF($2^m$) Addition',

qualtran/bloqs/gf_arithmetic/__init__.py

@@ -15,5 +15,8 @@
 from qualtran.bloqs.gf_arithmetic.gf2_add_k import GF2AddK
 from qualtran.bloqs.gf_arithmetic.gf2_addition import GF2Addition
 from qualtran.bloqs.gf_arithmetic.gf2_inverse import GF2Inverse
-from qualtran.bloqs.gf_arithmetic.gf2_multiplication import GF2Multiplication
+from qualtran.bloqs.gf_arithmetic.gf2_multiplication import (
+    GF2Multiplication,
+    MultiplyPolyByConstantMod,
+)
 from qualtran.bloqs.gf_arithmetic.gf2_square import GF2Square

qualtran/bloqs/gf_arithmetic/gf2_multiplication.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "87c95c4a",
+   "id": "f2e9ace3",
    "metadata": {
     "cq.autogen": "title_cell"
    },
@@ -13,7 +13,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31c1f087",
+   "id": "84523966",
    "metadata": {
     "cq.autogen": "top_imports"
    },
@@ -30,7 +30,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "307679ec",
+   "id": "d77b58bc",
    "metadata": {
     "cq.autogen": "GF2Multiplication.bloq_doc.md"
    },
@@ -72,7 +72,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "872a44d1",
+   "id": "40013f0c",
    "metadata": {
     "cq.autogen": "GF2Multiplication.bloq_doc.py"
    },
@@ -83,7 +83,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0f0db7d",
+   "id": "c5bcc7f0",
    "metadata": {
     "cq.autogen": "GF2Multiplication.example_instances.md"
    },
@@ -94,7 +94,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "131bc962",
+   "id": "75114297",
    "metadata": {
     "cq.autogen": "GF2Multiplication.gf16_multiplication"
    },
@@ -106,7 +106,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69f564d8",
+   "id": "7bdc2588",
    "metadata": {
     "cq.autogen": "GF2Multiplication.gf2_multiplication_symbolic"
    },
@@ -120,7 +120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a62c2b8",
+   "id": "9866335a",
    "metadata": {
     "cq.autogen": "GF2Multiplication.graphical_signature.md"
    },
@@ -131,7 +131,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf003e98",
+   "id": "f09a13f8",
    "metadata": {
     "cq.autogen": "GF2Multiplication.graphical_signature.py"
    },
@@ -144,7 +144,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f14ef0c5",
+   "id": "b26814e0",
    "metadata": {
     "cq.autogen": "GF2Multiplication.call_graph.md"
    },
@@ -155,7 +155,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f4b7bf2c",
+   "id": "7219fea5",
    "metadata": {
     "cq.autogen": "GF2Multiplication.call_graph.py"
    },
@@ -166,6 +166,112 @@
     "show_call_graph(gf16_multiplication_g)\n",
     "show_counts_sigma(gf16_multiplication_sigma)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9729be2",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.bloq_doc.md"
+   },
+   "source": [
+    "## `MultiplyPolyByConstantMod`\n",
+    "Multiply a polynomial by $f(x)$ modulu $m(x)$. Both $f(x)$ and $m(x)$ are constants.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `f_x`: The polynomial to mulitply with, given either a galois.Poly or as a sequence degrees.\n",
+    " - `m_x`: The modulus polynomial, given either a galois.Poly or as a sequence degrees. \n",
+    "\n",
+    "#### Registers\n",
+    " - `g`: The polynomial coefficients (in GF(2)). \n",
+    "\n",
+    "#### References\n",
+    " - [Space-efficient quantum multiplication of polynomials for binary finite fields with     sub-quadratic Toffoli gate count](https://arxiv.org/abs/1910.02849v2). Algorithm 1\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a25c2e49",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.gf_arithmetic import MultiplyPolyByConstantMod"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3690dcdb",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dffa638f",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.gf2_multiply_by_constant_modulu"
+   },
+   "outputs": [],
+   "source": [
+    "fx = [2, 0]  # x^2 + 1\n",
+    "mx = [0, 1, 3]  # x^3 + x + 1\n",
+    "gf2_multiply_by_constant_modulu = MultiplyPolyByConstantMod(fx, mx)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e140ad12",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "501a0781",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([gf2_multiply_by_constant_modulu],\n",
+    "           ['`gf2_multiply_by_constant_modulu`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "292b96b9",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fad6337a",
+   "metadata": {
+    "cq.autogen": "MultiplyPolyByConstantMod.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "gf2_multiply_by_constant_modulu_g, gf2_multiply_by_constant_modulu_sigma = gf2_multiply_by_constant_modulu.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(gf2_multiply_by_constant_modulu_g)\n",
+    "show_counts_sigma(gf2_multiply_by_constant_modulu_sigma)"
+   ]
   }
  ],
  "metadata": {

qualtran/bloqs/gf_arithmetic/gf2_multiplication.py

@@ -33,7 +33,7 @@
 from qualtran.symbolics import ceil, is_symbolic, log2, Shaped, SymbolicInt
 
 if TYPE_CHECKING:
-    from qualtran import BloqBuilder, Soquet
+    from qualtran import BloqBuilder, Soquet, SoquetT
     from qualtran.resource_counting import BloqCountDictT, BloqCountT, SympySymbolAllocator
     from qualtran.simulation.classical_sim import ClassicalValT
 
@@ -247,3 +247,107 @@ def _gf2_multiplication_symbolic() -> GF2Multiplication:
 _GF2_MULTIPLICATION_DOC = BloqDocSpec(
     bloq_cls=GF2Multiplication, examples=(_gf16_multiplication, _gf2_multiplication_symbolic)
 )
+
+
+@attrs.frozen
+class MultiplyPolyByConstantMod(Bloq):
+    r"""Multiply a polynomial by $f(x)$ modulu $m(x)$. Both $f(x)$ and $m(x)$ are constants.
+
+    Args:
+        f_x: The polynomial to mulitply with, given either a galois.Poly or as
+            a sequence degrees.
+        m_x: The modulus polynomial, given either a galois.Poly or as
+            a sequence degrees.
+
+    Registers:
+        g: The polynomial coefficients (in GF(2)).
+
+    References:
+        [Space-efficient quantum multiplication of polynomials for binary finite fields with
+            sub-quadratic Toffoli gate count](https://arxiv.org/abs/1910.02849v2) Algorithm 1
+    """
+
+    f_x: Poly = attrs.field(converter=lambda x: x if isinstance(x, Poly) else Poly.Degrees(x))
+    m_x: Poly = attrs.field(converter=lambda x: x if isinstance(x, Poly) else Poly.Degrees(x))
+
+    def __attrs_post_init__(self):
+        assert self.m_x.is_irreducible()
+        assert self.f_x.degrees.max() < self.m_x.degrees.max()
+
+    @cached_property
+    def n(self):
+        return self.m_x.degrees.max()
+
+    @cached_property
+    def lup(self) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
+        """Returns the LUP decomposition of the matrix representing the operation.
+
+        If m_x is irreducible, then the operation y := (y*f_x)%m_x can be represented
+        by a full rank matrix that can be decomposed into PLU where L and U are lower
+        and upper traingular matricies and P is a permutation matrix.
+        """
+        n = self.n
+        matrix = np.zeros((n, n), dtype=int)
+        for i in range(n):
+            p = (self.f_x * Poly.Degrees([i])) % self.m_x
+            for j in p.nonzero_degrees:
+                matrix[j, i] = 1
+        P, L, U = GF(2)(matrix).plu_decompose()
+        return np.asarray(L, dtype=int), np.asarray(U, dtype=int), np.asarray(P, dtype=int)
+
+    @cached_property
+    def signature(self) -> 'Signature':
+        return Signature([Register('g', QBit(), shape=(self.n,))])
+
+    def on_classical_vals(self, g) -> Dict[str, 'ClassicalValT']:
+        p = (Poly(g[::-1], GF(2)) * self.f_x) % self.m_x
+        res = p.coefficients().tolist()
+        res = [0 for _ in range(self.n - len(res))] + res
+        res = res[::-1]
+        return {'g': res}
+
+    def build_composite_bloq(self, bb: 'BloqBuilder', g: 'SoquetT') -> Dict[str, 'SoquetT']:
+        L, U, P = self.lup
+        if is_symbolic(self.n):
+            raise DecomposeTypeError(f"Symbolic decomposition isn't supported for {self}")
+        assert isinstance(g, np.ndarray)
+        for i in range(self.n):
+            for j in range(i + 1, self.n):
+                if U[i, j]:
+                    g[j], g[i] = bb.add(CNOT(), ctrl=g[j], target=g[i])
+
+        for i in reversed(range(self.n)):
+            for j in reversed(range(i)):
+                if L[i, j]:
+                    g[j], g[i] = bb.add(CNOT(), ctrl=g[j], target=g[i])
+
+        column = [*range(self.n)]
+        for i in range(self.n):
+            for j in range(i + 1, self.n):
+                if P[i, column[j]]:
+                    g[i], g[j] = g[j], g[i]
+                    column[i], column[j] = column[j], column[i]
+        return {'g': g}
+
+    def build_call_graph(
+        self, ssa: 'SympySymbolAllocator'
+    ) -> Union['BloqCountDictT', Set['BloqCountT']]:
+        L, U, _ = self.lup
+        # The number of cnots is the number of non zero off-diagnoal entries in L and U.
+        cnots = np.sum(L) + np.sum(U) - 2 * self.n
+        if cnots:
+            return {CNOT(): cnots}
+        return {}
+
+
+@bloq_example
+def _gf2_multiply_by_constant_modulu() -> MultiplyPolyByConstantMod:
+    fx = [2, 0]  # x^2 + 1
+    mx = [0, 1, 3]  # x^3 + x + 1
+    gf2_multiply_by_constant_modulu = MultiplyPolyByConstantMod(fx, mx)
+    return gf2_multiply_by_constant_modulu
+
+
+_MULTIPLY_BY_CONSTANT_MOD_DOC = BloqDocSpec(
+    bloq_cls=MultiplyPolyByConstantMod, examples=(_gf2_multiply_by_constant_modulu,)
+)