Create a bloq for galois multiplication

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

@@ -911,7 +911,7 @@ class QGF(QDType):
     characteristic: SymbolicInt
     degree: SymbolicInt
     irreducible_poly: Optional['galois.Poly'] = attrs.field()
-    element_repr: Literal["int", "poly", "power"] = attrs.field(default='int')
+    element_repr: Literal["int", "poly", "power"] = attrs.field(default='int', eq=False)
 
     @irreducible_poly.default
     def _irreducible_poly_default(self):

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,
+    GF2Mul,
     GF2Multiplication,
     GF2MultiplyByConstantMod,
+    GF2ShiftRightMod,
     MultiplyPolyByOnePlusXk,
 )
 from qualtran.bloqs.gf_arithmetic.gf2_square import GF2Square

qualtran/bloqs/gf_arithmetic/gf2_multiplication.ipynb

@@ -224,7 +224,7 @@
     "mx = galois.Poly.Degrees([0, 1, 3])  # x^3 + x + 1\n",
     "gf = galois.GF(2, 3, irreducible_poly=mx)\n",
     "const = gf(5)  # x^2 + 1\n",
-    "gf2_multiply_by_constant_modulu = GF2MultiplyByConstantMod(const, gf)"
+    "gf2_multiply_by_constant_modulu = GF2MultiplyByConstantMod(const, mx)"
    ]
   },
   {
@@ -521,6 +521,233 @@
     "show_call_graph(binarypolynomialmultiplication_g)\n",
     "show_counts_sigma(binarypolynomialmultiplication_sigma)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b87fb848",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.bloq_doc.md"
+   },
+   "source": [
+    "## `GF2ShiftRightMod`\n",
+    "Multiplies by $2^k$ (or $x^k$ for polynomials) modulu.\n",
+    "\n",
+    "Applies the transformation\n",
+    "$$\n",
+    "    \\ket{f} \\rightarrow \\ket{x^k f \\mod m(x)}\n",
+    "$$\n",
+    "\n",
+    "Where the modulus $m(x)$ is the irreducible polynomial defining the galois field arithmetic.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `m_x`: The irreducible polynomial that defines the galois field.\n",
+    " - `k`: The number of shifts (i.e. the exponent of $2$ or $x$). \n",
+    "\n",
+    "#### Registers\n",
+    " - `f`: The number (polynomial) to shift. \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). Section 3.1\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e359bb95",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.gf_arithmetic import GF2ShiftRightMod"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48528f04",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5de95a16",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.gf2shiftrightmod"
+   },
+   "outputs": [],
+   "source": [
+    "m_x = [5, 2, 0]  # x^5 + x^2 + 1\n",
+    "gf2shiftrightmod = GF2ShiftRightMod(m_x=m_x, k=3)  # shift by 3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8716920",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8b2a99b7",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([gf2shiftrightmod],\n",
+    "           ['`gf2shiftrightmod`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30d7d6b7",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b083b133",
+   "metadata": {
+    "cq.autogen": "GF2ShiftRightMod.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "gf2shiftrightmod_g, gf2shiftrightmod_sigma = gf2shiftrightmod.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(gf2shiftrightmod_g)\n",
+    "show_counts_sigma(gf2shiftrightmod_sigma)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ff7fda61",
+   "metadata": {
+    "cq.autogen": "GF2Mul.bloq_doc.md"
+   },
+   "source": [
+    "## `GF2Mul`\n",
+    "Multiplies two GF($2^n$) numbers (or binary polynomials) modulu.\n",
+    "\n",
+    "Applies the transformation\n",
+    "$$\n",
+    "    \\ket{f}\\ket{g} \\rightarrow \\ket{f} \\ket{g} \\ket{f*g \\mod m(x)}\n",
+    "$$\n",
+    "\n",
+    "Where the modulus $m(x)$ is the irreducible polynomial defining the galois field arithmetic.\n",
+    "The toffoli complexity is $n^{\\log_2{3}}$\n",
+    "\n",
+    "#### Parameters\n",
+    " - `m_x`: The irreducible polynomial that defines the galois field.\n",
+    " - `uncompute`: Whether to compute or uncompute the product. \n",
+    "\n",
+    "#### Registers\n",
+    " - `f`: The first number (polynomial).\n",
+    " - `g`: The second number (polynomial).\n",
+    " - `h`: The result. \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 4.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3fbbb423",
+   "metadata": {
+    "cq.autogen": "GF2Mul.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.gf_arithmetic import GF2Mul"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5080df63",
+   "metadata": {
+    "cq.autogen": "GF2Mul.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "97fb47ec",
+   "metadata": {
+    "cq.autogen": "GF2Mul.gf2mul"
+   },
+   "outputs": [],
+   "source": [
+    "m_x = [5, 2, 0]  # x^5 + x^2 + 1\n",
+    "gf2mul = GF2Mul(m_x=m_x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f7775fe5",
+   "metadata": {
+    "cq.autogen": "GF2Mul.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "55b3ab62",
+   "metadata": {
+    "cq.autogen": "GF2Mul.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([gf2mul],\n",
+    "           ['`gf2mul`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c41a8e24",
+   "metadata": {
+    "cq.autogen": "GF2Mul.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fcccc225",
+   "metadata": {
+    "cq.autogen": "GF2Mul.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "gf2mul_g, gf2mul_sigma = gf2mul.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(gf2mul_g)\n",
+    "show_counts_sigma(gf2mul_sigma)"
+   ]
   }
  ],
  "metadata": {