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Add SparseMatrixHermitian block-encoding (#1479)
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‎dev_tools/qualtran_dev_tools/notebook_specs.py

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import qualtran.bloqs.block_encoding.phase
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import qualtran.bloqs.block_encoding.product
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import qualtran.bloqs.block_encoding.sparse_matrix
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import qualtran.bloqs.block_encoding.sparse_matrix_hermitian
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import qualtran.bloqs.block_encoding.tensor_product
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import qualtran.bloqs.block_encoding.unitary
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import qualtran.bloqs.bookkeeping
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module=qualtran.bloqs.block_encoding.sparse_matrix,
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bloq_specs=[qualtran.bloqs.block_encoding.sparse_matrix._SPARSE_MATRIX_DOC],
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),
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NotebookSpecV2(
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title='Sparse Matrix Hermitian',
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module=qualtran.bloqs.block_encoding.sparse_matrix_hermitian,
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bloq_specs=[
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qualtran.bloqs.block_encoding.sparse_matrix_hermitian._SPARSE_MATRIX_HERMITIAN_DOC
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],
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),
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NotebookSpecV2(
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title='Chebyshev Polynomial',
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module=qualtran.bloqs.block_encoding.chebyshev_polynomial,

‎docs/bloqs/index.rst

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block_encoding/phase.ipynb
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block_encoding/linear_combination.ipynb
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block_encoding/sparse_matrix.ipynb
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block_encoding/sparse_matrix_hermitian.ipynb
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block_encoding/chebyshev_polynomial.ipynb
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block_encoding/lcu_block_encoding.ipynb
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‎qualtran/bloqs/block_encoding/__init__.py

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from qualtran.bloqs.block_encoding.phase import Phase
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from qualtran.bloqs.block_encoding.product import Product
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from qualtran.bloqs.block_encoding.sparse_matrix import SparseMatrix
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from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import SparseMatrixHermitian
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from qualtran.bloqs.block_encoding.tensor_product import TensorProduct
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from qualtran.bloqs.block_encoding.unitary import Unitary

‎qualtran/bloqs/block_encoding/sparse_matrix_hermitian.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "8e5e678f",
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"metadata": {
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"cq.autogen": "title_cell"
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},
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"source": [
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"# Sparse Matrix Hermitian"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "70980f2b",
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"metadata": {
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"cq.autogen": "top_imports"
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},
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"outputs": [],
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"source": [
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"from qualtran import Bloq, CompositeBloq, BloqBuilder, Signature, Register\n",
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"from qualtran import QBit, QInt, QUInt, QAny\n",
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"from qualtran.drawing import show_bloq, show_call_graph, show_counts_sigma\n",
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"from typing import *\n",
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"import numpy as np\n",
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"import sympy\n",
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"import cirq"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8db414b7",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.bloq_doc.md"
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},
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"source": [
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"## `SparseMatrixHermitian`\n",
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"Hermitian Block encoding of a sparse-access Hermitian matrix.\n",
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"\n",
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"Given column and entry oracles $O_c$ and $O_A$ for an $s$-sparse Hermitian matrix\n",
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"$A \\in \\mathbb{C}^{2^n \\times 2^n}$, i.e. one where each row / column has exactly $s$ non-zero\n",
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"entries, computes a $(s, n+1, \\epsilon)$-block encoding of $A$ as follows:\n",
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"```\n",
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" ┌────┐\n",
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"a |0> ─┤ ├─ |0> ───────────────────────X────────────────────\n",
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" │ │ ┌──┐ | ┌──┐\n",
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" │ U │ = │ n│ ┌────┐ ┌────┐ | ┌────┐ ┌────┐ │ n│\n",
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"l |0^n> ─┤ A ├─ |0^n> ─┤H ├─┤ O ├─┤ ├─X──|─┤ ├─┤ O* ├─┤H ├─\n",
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" │ │ └──┘ | c | │ │ | | │ │ | c | └──┘\n",
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" │ │ └────┘ │ O │ │ | │ O* │ └────┘\n",
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"b |0> ─┤ ├─ |0> ────────|────┤ A ├─|──X─┤ A ├───|─────────\n",
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" | | ┌────┐ | | | | | ┌────┐\n",
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" | | | O | | | | | | | O* |\n",
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"j |Psi> ─┤ ├─ |Psi> ──────┤ c ├─┤ ├─X────┤ ├─┤ c ├──────\n",
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" └────┘ └────┘ └────┘ └────┘ └────┘\n",
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"```\n",
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"\n",
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"To encode a matrix of irregular dimension, the matrix should first be embedded into one of\n",
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"dimension $2^n \\times 2^n$ for suitable $n$.\n",
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"To encode a matrix where each row / column has at most $s$ non-zero entries, some zeroes should\n",
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"be treated as if they were non-zero so that each row / column has exactly $s$ non-zero entries.\n",
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"\n",
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"For encoding a non-hermitian matrix, or a slightly more efficient (but non Hermitian-encoding)\n",
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"of a matrix, use :class:`SparseMatrix` instead.\n",
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"\n",
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"#### Parameters\n",
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" - `col_oracle`: The column oracle $O_c$. See `RowColumnOracle` for definition.\n",
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" - `entry_oracle`: The entry oracle $O_A$. See `EntryOracle` for definition.\n",
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" - `eps`: The precision of the block encoding.\n",
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" - `is_controlled`: if True, returns the controlled block-encoding. \n",
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"\n",
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"#### Registers\n",
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" - `ctrl`: The single qubit control register. (present only if `is_controlled` is `True`)\n",
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" - `system`: The system register.\n",
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" - `ancilla`: The ancilla register.\n",
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" - `resource`: The resource register (present only if `bitsize > 0`). \n",
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"\n",
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"#### References\n",
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" - [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"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f31bfd74",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.bloq_doc.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.block_encoding import SparseMatrixHermitian"
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]
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},
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{
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"cell_type": "markdown",
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"id": "435f31d2",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.example_instances.md"
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},
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"source": [
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"### Example Instances"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "720f3f9b",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.sparse_matrix_symb_hermitian_block_encoding"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.block_encoding.sparse_matrix import TopLeftRowColumnOracle\n",
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"from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import UniformSqrtEntryOracle\n",
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"\n",
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"n = sympy.Symbol('n', positive=True, integer=True)\n",
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"col_oracle = TopLeftRowColumnOracle(system_bitsize=n)\n",
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"entry_oracle = UniformSqrtEntryOracle(system_bitsize=n, entry=0.3)\n",
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"sparse_matrix_symb_hermitian_block_encoding = SparseMatrixHermitian(\n",
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" col_oracle, entry_oracle, eps=0\n",
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")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "70e512ff",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.sparse_matrix_hermitian_block_encoding"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.block_encoding.sparse_matrix import TopLeftRowColumnOracle\n",
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"from qualtran.bloqs.block_encoding.sparse_matrix_hermitian import UniformSqrtEntryOracle\n",
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"\n",
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"col_oracle = TopLeftRowColumnOracle(system_bitsize=2)\n",
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"entry_oracle = UniformSqrtEntryOracle(system_bitsize=2, entry=0.3)\n",
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"sparse_matrix_hermitian_block_encoding = SparseMatrixHermitian(col_oracle, entry_oracle, eps=0)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6e8d3efa",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.graphical_signature.md"
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},
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"source": [
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"#### Graphical Signature"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "96d58575",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.graphical_signature.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.drawing import show_bloqs\n",
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"show_bloqs([sparse_matrix_symb_hermitian_block_encoding, sparse_matrix_hermitian_block_encoding],\n",
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" ['`sparse_matrix_symb_hermitian_block_encoding`', '`sparse_matrix_hermitian_block_encoding`'])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e0108dfc",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.call_graph.md"
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},
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"source": [
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"### Call Graph"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "87933b2f",
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"metadata": {
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"cq.autogen": "SparseMatrixHermitian.call_graph.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.resource_counting.generalizers import ignore_split_join\n",
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"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",
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"show_call_graph(sparse_matrix_symb_hermitian_block_encoding_g)\n",
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"show_counts_sigma(sparse_matrix_symb_hermitian_block_encoding_sigma)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"name": "python"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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