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SparseMatrixHermitian block-encoding
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qualtran/bloqs/block_encoding/sparse_matrix_hermitian.ipynb
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "8e5e678f", | ||
| "metadata": { | ||
| "cq.autogen": "title_cell" | ||
| }, | ||
| "source": [ | ||
| "# Sparse Matrix Hermitian" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "70980f2b", | ||
| "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": "8db414b7", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.bloq_doc.md" | ||
| }, | ||
| "source": [ | ||
| "## `SparseMatrixHermitian`\n", | ||
| "Hermitian Block encoding of a sparse-access Hermitian matrix.\n", | ||
| "\n", | ||
| "Given column and entry oracles $O_c$ and $O_A$ for an $s$-sparse Hermitian 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", | ||
| "a |0> ─┤ ├─ |0> ───────────────────────X────────────────────\n", | ||
| " │ │ ┌──┐ | ┌──┐\n", | ||
| " │ U │ = │ n│ ┌────┐ ┌────┐ | ┌────┐ ┌────┐ │ n│\n", | ||
| "l |0^n> ─┤ A ├─ |0^n> ─┤H ├─┤ O ├─┤ ├─X──|─┤ ├─┤ O* ├─┤H ├─\n", | ||
| " │ │ └──┘ | c | │ │ | | │ │ | c | └──┘\n", | ||
| " │ │ └────┘ │ O │ │ | │ O* │ └────┘\n", | ||
| "b |0> ─┤ ├─ |0> ────────|────┤ A ├─|──X─┤ A ├───|─────────\n", | ||
| " | | ┌────┐ | | | | | ┌────┐\n", | ||
| " | | | O | | | | | | | O* |\n", | ||
| "j |Psi> ─┤ ├─ |Psi> ──────┤ c ├─┤ ├─X────┤ ├─┤ c ├──────\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", | ||
| "For encoding a non-hermitian matrix, or a slightly more efficient (but non Hermitian-encoding)\n", | ||
| "of a matrix, use :class:`SparseMatrix` instead.\n", | ||
| "\n", | ||
| "#### Parameters\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", | ||
| " - `is_controlled`: if True, returns the controlled block-encoding. \n", | ||
| "\n", | ||
| "#### Registers\n", | ||
| " - `ctrl`: The single qubit control register. (present only if `is_controlled` is `True`)\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/abs/2201.08309). Lin Lin (2022). Ch. 6.5. Proposition 6.8, Fig 6.7.\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "f31bfd74", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.bloq_doc.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.bloqs.block_encoding import SparseMatrixHermitian" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "435f31d2", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.example_instances.md" | ||
| }, | ||
| "source": [ | ||
| "### Example Instances" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "720f3f9b", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.sparse_matrix_symb_hermitian_block_encoding" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.bloqs.block_encoding.sparse_matrix import TopLeftRowColumnOracle\n", | ||
| "from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import UniformSqrtEntryOracle\n", | ||
| "\n", | ||
| "n = sympy.Symbol('n', positive=True, integer=True)\n", | ||
| "col_oracle = TopLeftRowColumnOracle(system_bitsize=n)\n", | ||
| "entry_oracle = UniformSqrtEntryOracle(system_bitsize=n, entry=0.3)\n", | ||
| "sparse_matrix_symb_hermitian_block_encoding = SparseMatrixHermitian(\n", | ||
| " col_oracle, entry_oracle, eps=0\n", | ||
| ")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "70e512ff", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.sparse_matrix_hermitian_block_encoding" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.bloqs.block_encoding.sparse_matrix import TopLeftRowColumnOracle\n", | ||
| "from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import UniformSqrtEntryOracle\n", | ||
| "\n", | ||
| "col_oracle = TopLeftRowColumnOracle(system_bitsize=2)\n", | ||
| "entry_oracle = UniformSqrtEntryOracle(system_bitsize=2, entry=0.3)\n", | ||
| "sparse_matrix_hermitian_block_encoding = SparseMatrixHermitian(col_oracle, entry_oracle, eps=0)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "6e8d3efa", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.graphical_signature.md" | ||
| }, | ||
| "source": [ | ||
| "#### Graphical Signature" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "96d58575", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.graphical_signature.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.drawing import show_bloqs\n", | ||
| "show_bloqs([sparse_matrix_symb_hermitian_block_encoding, sparse_matrix_hermitian_block_encoding],\n", | ||
| " ['`sparse_matrix_symb_hermitian_block_encoding`', '`sparse_matrix_hermitian_block_encoding`'])" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "e0108dfc", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.call_graph.md" | ||
| }, | ||
| "source": [ | ||
| "### Call Graph" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "87933b2f", | ||
| "metadata": { | ||
| "cq.autogen": "SparseMatrixHermitian.call_graph.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.resource_counting.generalizers import ignore_split_join\n", | ||
| "sparse_matrix_symb_hermitian_block_encoding_g, sparse_matrix_symb_hermitian_block_encoding_sigma = sparse_matrix_symb_hermitian_block_encoding.call_graph(max_depth=1, generalizer=ignore_split_join)\n", | ||
| "show_call_graph(sparse_matrix_symb_hermitian_block_encoding_g)\n", | ||
| "show_counts_sigma(sparse_matrix_symb_hermitian_block_encoding_sigma)" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "name": "python" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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