Create SparseMatrix block encoding

Author: charlesyuan314

dev_tools/autogenerate-bloqs-notebooks-v2.py

@@ -610,6 +610,7 @@
             qualtran.bloqs.block_encoding.product._PRODUCT_DOC,
             qualtran.bloqs.block_encoding.linear_combination._LINEAR_COMBINATION_DOC,
             qualtran.bloqs.block_encoding.phase._PHASE_DOC,
+            qualtran.bloqs.block_encoding.sparse_matrix._SPARSE_MATRIX_DOC,
         ],
         directory=f'{SOURCE_DIR}/bloqs/block_encoding/',
     ),

qualtran/bloqs/block_encoding/__init__.py

@@ -24,5 +24,6 @@
 from qualtran.bloqs.block_encoding.linear_combination import LinearCombination
 from qualtran.bloqs.block_encoding.phase import Phase
 from qualtran.bloqs.block_encoding.product import Product
+from qualtran.bloqs.block_encoding.sparse_matrix import SparseMatrix
 from qualtran.bloqs.block_encoding.tensor_product import TensorProduct
 from qualtran.bloqs.block_encoding.unitary import Unitary

qualtran/bloqs/block_encoding/block_encoding.ipynb

@@ -1304,6 +1304,141 @@
     "show_call_graph(linear_combination_block_encoding_g)\n",
     "show_counts_sigma(linear_combination_block_encoding_sigma)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e36b6098",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.bloq_doc.md"
+   },
+   "source": [
+    "## `SparseMatrix`\n",
+    "Block encoding of a sparse-access matrix.\n",
+    "\n",
+    "Given row, column, and entry oracles $O_r$, $O_c$, and $O_A$ for an $s$-sparse matrix\n",
+    "$A \\in \\mathbb{C}^{2^n \\times 2^n}$, i.e. one where each row / column has exactly $s$ non-zero\n",
+    "entries, computes a $(s, n+1, \\epsilon)$-block encoding of $A$ as follows:\n",
+    "```\n",
+    "       ┌────┐                       ┌────┐\n",
+    "  |0> ─┤    ├─     |0> ─────────────┤    ├───────────────\n",
+    "       │    │           ┌──┐        │    │          ┌──┐\n",
+    "       │ U  │  =        │ n│ ┌────┐ │ O  │   ┌────┐ │ n│\n",
+    "|0^n> ─┤  A ├─   |0^n> ─┤H ├─┤    ├─┤  A ├─X─┤    ├─┤H ├─\n",
+    "       │    │           └──┘ │ O  │ │    │ │ │ O* │ └──┘\n",
+    "|Psi> ─┤    ├─   |Psi> ──────┤  c ├─┤    ├─X─┤  r ├──────\n",
+    "       └────┘                └────┘ └────┘   └────┘\n",
+    "```\n",
+    "\n",
+    "To encode a matrix of irregular dimension, the matrix should first be embedded into one of\n",
+    "dimension $2^n \\times 2^n$ for suitable $n$.\n",
+    "To encode a matrix where each row / column has at most $s$ non-zero entries, some zeroes should\n",
+    "be treated as if they were non-zero so that each row / column has exactly $s$ non-zero entries.\n",
+    "\n",
+    "#### Parameters\n",
+    " - `row_oracle`: The row oracle $O_r$. See `RowColumnOracle` for definition.\n",
+    " - `col_oracle`: The column oracle $O_c$. See `RowColumnOracle` for definition.\n",
+    " - `entry_oracle`: The entry oracle $O_A$. See `EntryOracle` for definition.\n",
+    " - `eps`: The precision of the block encoding. \n",
+    "\n",
+    "#### Registers\n",
+    " - `system`: The system register.\n",
+    " - `ancilla`: The ancilla register.\n",
+    " - `resource`: The resource register (present only if bitsize > 0). \n",
+    "\n",
+    "#### References\n",
+    " - [Lecture Notes on Quantum Algorithms for Scientific Computation]( https://arxiv.org/pdf/2201.08309). Lin Lin (2022). Ch. 6.5.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "87710c02",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.bloq_doc.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.block_encoding import SparseMatrix"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b9bd4f0",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.example_instances.md"
+   },
+   "source": [
+    "### Example Instances"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6ad71b09",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.sparse_matrix_block_encoding"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.bloqs.block_encoding.sparse_matrix import (\n",
+    "    UniformEntryOracle,\n",
+    "    UniformRowColumnOracle,\n",
+    ")\n",
+    "\n",
+    "row_oracle = UniformRowColumnOracle(n=2, num_nonzero=4)\n",
+    "col_oracle = UniformRowColumnOracle(n=2, num_nonzero=4)\n",
+    "entry_oracle = UniformEntryOracle(n=2, entry=0.3)\n",
+    "sparse_matrix_block_encoding = SparseMatrix(row_oracle, col_oracle, entry_oracle, eps=0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca16f4df",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.graphical_signature.md"
+   },
+   "source": [
+    "#### Graphical Signature"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6c5da6eb",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.graphical_signature.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.drawing import show_bloqs\n",
+    "show_bloqs([sparse_matrix_block_encoding],\n",
+    "           ['`sparse_matrix_block_encoding`'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "847bacb4",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.call_graph.md"
+   },
+   "source": [
+    "### Call Graph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "42070c26",
+   "metadata": {
+    "cq.autogen": "SparseMatrix.call_graph.py"
+   },
+   "outputs": [],
+   "source": [
+    "from qualtran.resource_counting.generalizers import ignore_split_join\n",
+    "sparse_matrix_block_encoding_g, sparse_matrix_block_encoding_sigma = sparse_matrix_block_encoding.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
+    "show_call_graph(sparse_matrix_block_encoding_g)\n",
+    "show_counts_sigma(sparse_matrix_block_encoding_sigma)"
+   ]
   }
  ],
  "metadata": {