Create KaliskiModInverse (#1464)

* Create KaliskiModInverse * format * change signature * free * use half comp * Add documentation * nit * address comments * type * update classical action * nit --------- Co-authored-by: Matthew Harrigan <[email protected]>
quantumlib · Oct 30, 2024 · b3e0748 · b3e0748
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diff --git a/dev_tools/qualtran_dev_tools/notebook_specs.py b/dev_tools/qualtran_dev_tools/notebook_specs.py
@@ -520,6 +520,11 @@
             qualtran.bloqs.mod_arithmetic.mod_multiplication._DIRTY_OUT_OF_PLACE_MONTGOMERY_MOD_MUL_DOC,
         ],
     ),
+    NotebookSpecV2(
+        title='Modular Divison',
+        module=qualtran.bloqs.mod_arithmetic.mod_division,
+        bloq_specs=[qualtran.bloqs.mod_arithmetic.mod_division._KALISKI_MOD_INVERSE_DOC],
+    ),
     NotebookSpecV2(
         title='Factoring RSA',
         module=qualtran.bloqs.factoring.rsa,

diff --git a/docs/bloqs/index.rst b/docs/bloqs/index.rst
@@ -83,6 +83,7 @@ Bloqs Library
     mod_arithmetic/mod_addition.ipynb
     mod_arithmetic/mod_subtraction.ipynb
     mod_arithmetic/mod_multiplication.ipynb
+    mod_arithmetic/mod_division.ipynb
     factoring/rsa/rsa.ipynb
     factoring/ecc/ec_add.ipynb
     factoring/ecc/ecc.ipynb

diff --git a/qualtran/bloqs/mod_arithmetic/__init__.py b/qualtran/bloqs/mod_arithmetic/__init__.py
@@ -14,5 +14,6 @@
 
 from ._shims import ModInv
 from .mod_addition import CModAdd, CModAddK, CtrlScaleModAdd, ModAdd, ModAddK
+from .mod_division import KaliskiModInverse
 from .mod_multiplication import CModMulK, DirtyOutOfPlaceMontgomeryModMul, ModDbl
 from .mod_subtraction import CModNeg, CModSub, ModNeg, ModSub
diff --git a/qualtran/bloqs/mod_arithmetic/mod_division.ipynb b/qualtran/bloqs/mod_arithmetic/mod_division.ipynb
@@ -0,0 +1,170 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "1c5f2b28",
+   "metadata": {
+    "cq.autogen": "title_cell"
+   },
+   "source": [
+    "# Modular Divison"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8751aa36",
+   "metadata": {
+    "cq.autogen": "top_imports"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
+    "from qualtran import QBit, QInt, QUInt, QAny\n",
+    "from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
+    "from typing import *\n",
+    "import numpy as np\n",
+    "import sympy\n",
+    "import cirq"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d680443c",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.bloq_doc.md"
+   },
+   "source": [
+    "## `KaliskiModInverse`\n",
+    "Compute modular multiplicative inverse -inplace- of numbers in montgomery form.\n",
+    "\n",
+    "Applies the transformation\n",
+    "$$\n",
+    "    \\ket{x} \\ket{0} \\rightarrow \\ket{x^{-1} 2^{2n} \\mod p} \\ket{\\mathrm{garbage}}\n",
+    "$$\n",
+    "\n",
+    "#### Parameters\n",
+    " - `bitsize`: size of the number.\n",
+    " - `mod`: The integer modulus.\n",
+    " - `uncompute`: whether to compute or uncompute. \n",
+    "\n",
+    "#### Registers\n",
+    " - `x`: The register for which we compute the multiplicative inverse.\n",
+    " - `m`: A 2*bitsize register of intermediate values needed for uncomputation. \n",
+    "\n",
+    "#### References\n",
+    " - [Performance Analysis of a Repetition Cat Code Architecture: Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126 133 Cat Qubits](https://arxiv.org/abs/2302.06639).     Appendix C5.\n",
+    " - [Improved quantum circuits for elliptic curve discrete logarithms](https://arxiv.org/abs/2001.09580).     Fig 7(b)\n",
+    " - [How to compute a 256-bit elliptic curve private key with only 50 million Toffoli gates](https://arxiv.org/abs/2306.08585).     page 8.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f5917d72",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.mod_arithmetic import KaliskiModInverse"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d44329eb",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31a37cf6",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.kaliskimodinverse_example"
+   },
+   "outputs": [],
+   "source": [
+    "kaliskimodinverse_example = KaliskiModInverse(32, 10**9 + 7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "58c697e6",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.kaliskimodinverse_symbolic"
+   },
+   "outputs": [],
+   "source": [
+    "n, p = sympy.symbols('n p')\n",
+    "kaliskimodinverse_symbolic = KaliskiModInverse(n, p)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9bf1e17c",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "eca3a706",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([kaliskimodinverse_example, kaliskimodinverse_symbolic],\n",
+    "           ['`kaliskimodinverse_example`', '`kaliskimodinverse_symbolic`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "69fd8906",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "15c6fabe",
+   "metadata": {
+    "cq.autogen": "KaliskiModInverse.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "kaliskimodinverse_example_g, kaliskimodinverse_example_sigma = kaliskimodinverse_example.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(kaliskimodinverse_example_g)\n",
+    "show_counts_sigma(kaliskimodinverse_example_sigma)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}