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anurudhpanurudhp
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planted noisy kXOR algorithm
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‎dev_tools/qualtran_dev_tools/notebook_specs.py‎

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import qualtran.bloqs.multiplexers.select_base
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import qualtran.bloqs.multiplexers.select_pauli_lcu
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import qualtran.bloqs.optimization.k_xor_sat
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import qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian
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import qualtran.bloqs.optimization.k_xor_sat.kikuchi_guiding_state
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import qualtran.bloqs.phase_estimation.lp_resource_state
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import qualtran.bloqs.phase_estimation.qubitization_qpe
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# ----- Optimization ---------------------------------------------------
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# --------------------------------------------------------------------------
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OPTIMIZATION: List[NotebookSpecV2] = [
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# ----- Preliminaries ------------------------------------------
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NotebookSpecV2(
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title='Guided (sparse) Hamiltonian Problem',
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module=qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian,
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bloq_specs=[
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qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_DOC,
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qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian.guided_hamiltonian._GUIDED_HAMILTONIAN_PHASE_ESTIMATION_DOC,
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],
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),
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# ----- Algorithm ------------------------------------------
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NotebookSpecV2(
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title='kXOR: Instance load Oracles',
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qualtran.bloqs.optimization.k_xor_sat.kikuchi_block_encoding._KIKUCHI_HAMILTONIAN_DOC
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],
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),
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NotebookSpecV2(
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title='Algorithm: Planted Noisy kXOR',
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module=qualtran.bloqs.optimization.k_xor_sat.planted_noisy_kxor,
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bloq_specs=[
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qualtran.bloqs.optimization.k_xor_sat.planted_noisy_kxor._PLANTED_NOISY_KXOR_DOC
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],
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),
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]
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# --------------------------------------------------------------------------

‎docs/bloqs/index.rst‎

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:maxdepth: 2
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:caption: Optimization:
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optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.ipynb
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optimization/k_xor_sat/load_kxor_instance.ipynb
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optimization/k_xor_sat/kikuchi_guiding_state.ipynb
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optimization/k_xor_sat/kikuchi_adjacency_list.ipynb
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optimization/k_xor_sat/kikuchi_adjacency_matrix.ipynb
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optimization/k_xor_sat/kikuchi_block_encoding.ipynb
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optimization/k_xor_sat/planted_noisy_kxor.ipynb
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.. toctree::
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:maxdepth: 2

‎qualtran/bloqs/optimization/k_xor_sat/__init__.py‎

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from .kikuchi_block_encoding import KikuchiHamiltonian, KikuchiMatrixEntry, KikuchiNonZeroIndex
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from .kikuchi_guiding_state import GuidingState, SimpleGuidingState
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from .kxor_instance import Constraint, KXorInstance
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from .planted_noisy_kxor import AliceTheorem, PlantedNoisyKXOR
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from .load_kxor_instance import LoadConstraintScopes, LoadUniqueScopeIndex, PRGAUniqueConstraintRHS

‎qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/__init__.py‎

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# Copyright 2024 Google LLC
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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from .guided_hamiltonian import GuidedHamiltonian, GuidedHamiltonianPhaseEstimation
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from .walk_operator import QubitizedWalkOperator

‎qualtran/bloqs/optimization/k_xor_sat/guided_hamiltonian/guided_hamiltonian.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": "e299e7a9",
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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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"# Guided (sparse) Hamiltonian Problem\n",
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"\n",
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"Section 4.4.2 Simulating the Kikuchi Hamiltonian\n",
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"\n",
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"This module contains oracles to implement the block-encoding of the Kikuchi\n",
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"Hamiltonian corresponding to an input k-XOR-SAT instance.\n",
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"\n",
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"References:\n",
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" [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1)\n",
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" Section 4.4.2 for algorithm. Section 2.4 for definitions and notation."
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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": "e2be674c",
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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": "8d10248d",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.bloq_doc.md"
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},
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"source": [
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"## `GuidedHamiltonian`\n",
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"Solve the guided (sparse) hamiltonian problem.\n",
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"\n",
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"Definition 4.8 (modified to accept any block-encoding):\n",
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"In the Guided Hamiltonian problem we are given the following as input:\n",
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"\n",
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"1. A $(\\sqrt{2} s, \\cdot, 0)$-block-encoding of a Hamiltonian $H$ such that $\\|H\\|_\\max \\le s$.\n",
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"2. A unitary program that prepares $|\\Psi\\rangle|0^A\\rangle$.\n",
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"3. Parameters $\\lambda \\in [-\\Lambda, \\Lambda]$, $\\alpha \\in (0, 1)$, $\\gamma \\in (0, 1]$.\n",
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"\n",
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"and we should output\n",
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"\n",
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"- YES (1) if $\\| \\Pi_{\\ge \\lambda} (H) |\\Psi\\rangle \\| \\ge \\gamma$\n",
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"- NO (0) if $\\|H\\| \\le (1 - \\alpha) \\lambda$\n",
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"\n",
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"Note that the above drops the sparse requirement, and accepts any\n",
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"$(\\alpha_H, \\cdot, \\cdot)$-block-encoding of $H$.\n",
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"In the sparse Hamiltonian case, $\\alpha_H = s$ (where $s$ is the sparsity).\n",
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"\n",
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"Algorithm (Theorem 4.9):\n",
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" This uses phase estimation on the block-encoding of $e^{iHt}$, and then uses\n",
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" amplitude amplification to increase the success probability to $1 - o(1)$.\n",
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"\n",
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"We instead directly do phase-estimation on the qubitized (Szegedy) walk operator for $H$\n",
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"\n",
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"#### Parameters\n",
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" - `hamiltonian`: the block-encoding of $H$\n",
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" - `guiding_state`: the unitary that prepares $|\\Psi\\rangle$\n",
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" - `lambd`: parameter $\\lambda$\n",
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" - `alpha`: parameter $\\alpha$\n",
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" - `gamma`: parameter $\\gamma$ \n",
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"\n",
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"#### References\n",
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" - [Quartic quantum speedups for planted inference](https://arxiv.org/abs/2406.19378v1). Section 4.2 \"Guided Sparse Hamiltonian Problem\".\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": "29d536c3",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.bloq_doc.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian import GuidedHamiltonian"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a216ac70",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.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": "fabf68e4",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.guided_hamiltonian"
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},
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"outputs": [],
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"source": [
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"import sympy\n",
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"\n",
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"from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance\n",
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"from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare\n",
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"from qualtran.symbolics import ceil, log2\n",
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"\n",
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"n, k, m, c = sympy.symbols(\"n k m c\", positive=True, integer=True)\n",
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"zeta = sympy.symbols(r\"\\zeta\", positive=True)\n",
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"\n",
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"inst_guide = KXorInstance.symbolic(n, (1 - zeta) * m, k, max_rhs=2)\n",
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"inst_solve = KXorInstance.symbolic(n, zeta * m, k, max_rhs=2)\n",
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"l = c * k\n",
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"s = l * ceil(log2(n))\n",
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"\n",
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"Psi = GuidingState(inst_guide, l)\n",
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"H = KikuchiHamiltonian(inst_solve, c * k, s)\n",
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"\n",
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"lambd, alpha, gamma = sympy.symbols(r\"\\lambda \\alpha \\gamma\", positive=True, real=True)\n",
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"guided_hamiltonian = GuidedHamiltonian(H, BlackBoxPrepare(Psi), lambd, alpha, gamma)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7ad9d994",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.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": "5ae17ad5",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.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([guided_hamiltonian],\n",
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" ['`guided_hamiltonian`'])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1b3e1663",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.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": "08946e48",
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"metadata": {
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"cq.autogen": "GuidedHamiltonian.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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"guided_hamiltonian_g, guided_hamiltonian_sigma = guided_hamiltonian.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
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"show_call_graph(guided_hamiltonian_g)\n",
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"show_counts_sigma(guided_hamiltonian_sigma)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "0b22b193",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.bloq_doc.md"
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},
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"source": [
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"## `GuidedHamiltonianPhaseEstimation`\n",
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"Implement the phase estimation algorithm $U_\\text{PE}$"
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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": "b3806eb0",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.bloq_doc.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.optimization.k_xor_sat.guided_hamiltonian import GuidedHamiltonianPhaseEstimation"
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]
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},
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{
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"cell_type": "markdown",
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"id": "500f891d",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.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": "bfdbf9a6",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.guided_phase_estimate_symb"
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},
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"outputs": [],
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"source": [
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"import sympy\n",
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"\n",
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"from qualtran.bloqs.optimization.k_xor_sat import GuidingState, KikuchiHamiltonian, KXorInstance\n",
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"from qualtran.bloqs.state_preparation.black_box_prepare import BlackBoxPrepare\n",
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"from qualtran.symbolics import ceil, log2\n",
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"\n",
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"n, k, c = sympy.symbols(\"n k c\", positive=True, integer=True)\n",
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"m_guide, m_solve = sympy.symbols(\"m_1 m_2\", positive=True, integer=True)\n",
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"\n",
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"inst_guide = KXorInstance.symbolic(n, m_guide, k, max_rhs=2)\n",
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"inst_solve = KXorInstance.symbolic(n, m_solve, k, max_rhs=2)\n",
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"l = c * k\n",
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"s = l * ceil(log2(n))\n",
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"\n",
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"Psi = GuidingState(inst_guide, l)\n",
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"H = KikuchiHamiltonian(inst_solve, c * k, s)\n",
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"\n",
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"eps, delta = sympy.symbols(r\"\\epsilon_{PE} \\delta_{PE}\", positive=True, real=True)\n",
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"guided_phase_estimate_symb = GuidedHamiltonianPhaseEstimation(\n",
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" H, BlackBoxPrepare(Psi), eps, delta\n",
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")\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d6408318",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.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": "3a1d74b2",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.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([guided_phase_estimate_symb],\n",
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" ['`guided_phase_estimate_symb`'])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a5d710cd",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.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": "749b6440",
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"metadata": {
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"cq.autogen": "GuidedHamiltonianPhaseEstimation.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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"guided_phase_estimate_symb_g, guided_phase_estimate_symb_sigma = guided_phase_estimate_symb.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
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"show_call_graph(guided_phase_estimate_symb_g)\n",
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"show_counts_sigma(guided_phase_estimate_symb_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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