Implement Kikuchi graph oracles and block-encoding

dev_tools/qualtran_dev_tools/notebook_specs.py

@@ -104,6 +104,7 @@
 import qualtran.bloqs.multiplexers.black_box_select
 import qualtran.bloqs.multiplexers.select_base
 import qualtran.bloqs.multiplexers.select_pauli_lcu
+import qualtran.bloqs.optimization.k_xor_sat
 import qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state
 import qualtran.bloqs.phase_estimation.lp_resource_state
 import qualtran.bloqs.phase_estimation.qubitization_qpe
@@ -809,14 +810,41 @@
 # -----   Optimization   ---------------------------------------------------
 # --------------------------------------------------------------------------
 OPTIMIZATION: List[NotebookSpecV2] = [
+    # -----   Algorithm  ------------------------------------------
+    NotebookSpecV2(
+        title='kXOR: Instance load Oracles',
+        module=qualtran.bloqs.optimization.k_xor_sat.load_kxor_instance,
+        bloq_specs=[qualtran.bloqs.optimization.k_xor_sat.load_kxor_instance._LOAD_INSTANCE_DOC],
+    ),
     NotebookSpecV2(
         title='Planted Noisy kXOR - Kikuchi Guiding State',
         module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state,
         bloq_specs=[
             qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state._SIMPLE_GUIDING_STATE_DOC,
             qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state._GUIDING_STATE_DOC,
         ],
-    )
+    ),
+    NotebookSpecV2(
+        title='Planted Noisy kXOR: Kikuchi Adjacency List',
+        module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_list,
+        bloq_specs=[
+            qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_list._KIKUCHI_NONZERO_INDEX_DOC
+        ],
+    ),
+    NotebookSpecV2(
+        title='Planted Noisy kXOR: Kikuchi Adjacency Matrix',
+        module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_matrix,
+        bloq_specs=[
+            qualtran.bloqs.optimization.k_xor_sat.kikuchi_adjacency_matrix._KIKUCHI_MATRIX_ENTRY_DOC
+        ],
+    ),
+    NotebookSpecV2(
+        title='Planted Noisy kXOR: Block-encoding the Kikuchi Matrix',
+        module=qualtran.bloqs.optimization.k_xor_sat.kikuchi_block_encoding,
+        bloq_specs=[
+            qualtran.bloqs.optimization.k_xor_sat.kikuchi_block_encoding._KIKUCHI_HAMILTONIAN_DOC
+        ],
+    ),
 ]
 
 # --------------------------------------------------------------------------

docs/bloqs/index.rst

@@ -147,7 +147,11 @@ Bloqs Library
     :maxdepth: 2
     :caption: Optimization:
 
+    optimization/k_xor_sat/load_kxor_instance.ipynb
     optimization/k_xor_sat/kikuchi_guiding_state.ipynb
+    optimization/k_xor_sat/kikuchi_adjacency_list.ipynb
+    optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb
+    optimization/k_xor_sat/kikuchi_block_encoding.ipynb
 
 .. toctree::
     :maxdepth: 2

qualtran/bloqs/optimization/k_xor_sat/__init__.py

@@ -11,5 +11,9 @@
 #  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 #  See the License for the specific language governing permissions and
 #  limitations under the License.
+from .kikuchi_adjacency_list import KikuchiNonZeroIndex
+from .kikuchi_adjacency_matrix import KikuchiMatrixEntry
+from .kikuchi_block_encoding import KikuchiHamiltonian, KikuchiMatrixEntry, KikuchiNonZeroIndex
 from .kikuchi_guiding_state import GuidingState, SimpleGuidingState
 from .kxor_instance import Constraint, KXorInstance
+from .load_kxor_instance import LoadConstraintScopes, LoadUniqueScopeIndex, PRGAUniqueConstraintRHS

qualtran/bloqs/optimization/k_xor_sat/kikuchi_adjacency_list.ipynb

@@ -0,0 +1,180 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3c1703d8",
+   "metadata": {
+    "cq.autogen": "title_cell"
+   },
+   "source": [
+    "# Planted Noisy kXOR: Kikuchi Adjacency List"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ece15719",
+   "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": "c187b17d",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.bloq_doc.md"
+   },
+   "source": [
+    "## `KikuchiNonZeroIndex`\n",
+    "Adjacency list oracle $O_F$ for the Kikuchi matrix.\n",
+    "\n",
+    "The oracle $O_F$ (Definition 4.5) takes in $i, k$,\n",
+    "and outputs $i, f(i, k)$ where $f(i, k)$ is\n",
+    "index of the $k$-th non-zero entry in row $i$.\n",
+    "\n",
+    "As the Kikuchi matrix is symmetric, we can use the same oracle for both rows and columns.\n",
+    "\n",
+    "The Kikuchi matrix is indexed by $S \\in {[n] \\choose k}$.\n",
+    "For a given row $S$ and column $T$, the entry $\\mathcal{K}_{k}_{S, T}$\n",
+    "is potentially non-zero if $S \\Delta T = U_j$ for some $j$, which is\n",
+    "equivalent to $T = S \\Delta U_j$.\n",
+    "Here, $U_j$ is the $j$-th unique scope in the instance $\\mathcal{I}$.\n",
+    "\n",
+    "To find the $k$-th non-zero entry, we use two oracles:\n",
+    "1. $(S, k) \\mapsto f(S, k)$, implemented by `ColumnOfKthNonZeroEntry`\n",
+    "2. $(S, f(S, k)) \\mapsto k$, implemented by `IndexOfNonZeroColumn`.\n",
+    "\n",
+    "Both these above oracles are unitary: they do not have any entangled ancilla/junk registers.\n",
+    "\n",
+    "\n",
+    "Note on sparsity: This bloq expects the user to provide the sparsity, as it is in general\n",
+    "difficult to compute the precise sparsity of the Kikuchi matrix efficiently. As long as the\n",
+    "provided number is at least the true sparsity, the algorithm will work as expected.\n",
+    "In case the provides sparsity is smaller, it is equivalent to making the remaining entries zero in the final block encoding.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `inst`: the kXOR instance $\\mathcal{I}$.\n",
+    " - `ell`: Kikuchi parameter $\\ell$.\n",
+    " - `s`: sparsity, i.e. max number of non-zero entries in a row/column. \n",
+    "\n",
+    "#### Registers\n",
+    " - `i`: integer in [2^N]\n",
+    " - `k`: integer in [2^N] \n",
+    "\n",
+    "#### References\n",
+    " - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Theorem 4.17, proof para 4 (top of page 39).\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d329e657",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.optimization.k_xor_sat import KikuchiNonZeroIndex"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8516f446",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "409ea009",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.kikuchi_nonzero_index"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.optimization.k_xor_sat.kxor_instance import example_kxor_instance\n",
+    "\n",
+    "inst = example_kxor_instance()\n",
+    "ell = 8\n",
+    "s = inst.brute_force_sparsity(ell)\n",
+    "\n",
+    "kikuchi_nonzero_index = KikuchiNonZeroIndex(inst, ell, s=s)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c08eb466",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a7478a9a",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([kikuchi_nonzero_index],\n",
+    "           ['`kikuchi_nonzero_index`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e07ff5a",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "138befd7",
+   "metadata": {
+    "cq.autogen": "KikuchiNonZeroIndex.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "kikuchi_nonzero_index_g, kikuchi_nonzero_index_sigma = kikuchi_nonzero_index.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(kikuchi_nonzero_index_g)\n",
+    "show_counts_sigma(kikuchi_nonzero_index_sigma)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}