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Add KaiserWindowState bloq to prepare initial state for high confidence QPE (#1331)
* Add KaiserWindowState bloq * Address nits * Remove gate with registers
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‎dev_tools/autogenerate-bloqs-notebooks-v2.py‎

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qualtran.bloqs.phase_estimation.text_book_qpe._CC_TEXTBOOK_PHASE_ESTIMATION_DOC,
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],
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),
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NotebookSpecV2(
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title='Kaiser Window State for Quantum Phase Estimation',
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module=qualtran.bloqs.phase_estimation.kaiser_window_state,
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bloq_specs=[
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qualtran.bloqs.phase_estimation.kaiser_window_state._CC_KAISER_WINDOW_STATE_DOC
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],
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),
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NotebookSpecV2(
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title='Qubitization Walk Operator',
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module=qualtran.bloqs.qubitization.qubitization_walk_operator,

‎docs/bloqs/index.rst‎

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qft/qft_phase_gradient.ipynb
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phase_estimation/lp_resource_state.ipynb
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phase_estimation/text_book_qpe.ipynb
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phase_estimation/kaiser_window_state.ipynb
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qubitization/qubitization_walk_operator.ipynb
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phase_estimation/qubitization_qpe.ipynb
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‎qualtran/bloqs/phase_estimation/__init__.py‎

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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 qualtran.bloqs.phase_estimation.kaiser_window_state import KaiserWindowState
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from qualtran.bloqs.phase_estimation.lp_resource_state import LPResourceState
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from qualtran.bloqs.phase_estimation.qpe_window_state import RectangularWindowState
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from qualtran.bloqs.phase_estimation.qubitization_qpe import QubitizationQPE

‎qualtran/bloqs/phase_estimation/kaiser_window_state.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": "1cf5d12a",
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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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"# Kaiser Window State for Quantum Phase Estimation"
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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": "5e51f8aa",
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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": "afc0bf73",
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"metadata": {
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"cq.autogen": "KaiserWindowState.bloq_doc.md"
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},
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"source": [
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"## `KaiserWindowState`\n",
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"Bloq to prepare a Kaiser window state for high confidence Quantum Phase Estimation.\n",
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"\n",
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"Kaiser window states are optimal to minimize the probability of error outside a given\n",
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"confidence interval.\n",
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"Given the bitsize $m$ and parameter $\\alpha$, the bloq prepares an $m$-bit state with\n",
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"coefficients\n",
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"\n",
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"$$\n",
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" \\sum\\limits_{x=-M}^{M}\\frac{1}{2M} \\frac{I_0\\left(\\pi\\alpha\\sqrt{1-(x/M)^2}\\right)}{I_0\\left(\\pi\\alpha\\right)}\\ket{x}\n",
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"$$\n",
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"\n",
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"where $M = 2^{m-1}$. See Ref[1] for more details.\n",
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"\n",
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"\n",
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"#### Parameters\n",
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" - `bitsize`: Number of bits in the control register of QPE.\n",
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" - `alpha`: Shape parameter, determines trade-off between main-lobe width and side lobe level. \n",
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"\n",
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"#### References\n",
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" - [Analyzing Prospects for Quantum Advantage in Topological Data Analysis](https://arxiv.org/abs/2209.13581). Berry et. al. (2022). Appendix D\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": "a7069b8f",
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"metadata": {
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"cq.autogen": "KaiserWindowState.bloq_doc.py"
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},
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"outputs": [],
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"source": [
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"from qualtran.bloqs.phase_estimation.kaiser_window_state import KaiserWindowState"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e00a42ff",
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"metadata": {
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"cq.autogen": "KaiserWindowState.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": "07877dd0",
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"metadata": {
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"cq.autogen": "KaiserWindowState.kaiser_window_state_small"
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},
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"outputs": [],
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"source": [
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"kaiser_window_state_small = KaiserWindowState(5, 2)"
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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": "6fee6ed4",
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"metadata": {
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"cq.autogen": "KaiserWindowState.kaiser_window_state_symbolic"
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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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"kaiser_window_state_symbolic = KaiserWindowState(*sympy.symbols('n, alpha'))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "c61fccb5",
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"metadata": {
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"cq.autogen": "KaiserWindowState.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": "5fdaba20",
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"metadata": {
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"cq.autogen": "KaiserWindowState.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([kaiser_window_state_small, kaiser_window_state_symbolic],\n",
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" ['`kaiser_window_state_small`', '`kaiser_window_state_symbolic`'])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d41cf909",
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"metadata": {
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"cq.autogen": "KaiserWindowState.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": "189bcc85",
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"metadata": {
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"cq.autogen": "KaiserWindowState.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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"kaiser_window_state_small_g, kaiser_window_state_small_sigma = kaiser_window_state_small.call_graph(max_depth=1, generalizer=ignore_split_join)\n",
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"show_call_graph(kaiser_window_state_small_g)\n",
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"show_counts_sigma(kaiser_window_state_small_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": "19e7add5-c01c-4441-9f95-99f0475243f7",
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"metadata": {},
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"source": [
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"## Example of QPE comparing different window functions"
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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": "ef07f4b9-39ec-43d2-a11e-92f926a6e0e4",
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"metadata": {},
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"outputs": [],
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"source": [
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"import cirq\n",
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"import numpy as np\n",
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"from qualtran import BloqBuilder, CompositeBloq\n",
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"from qualtran.bloqs.basic_gates import ZPowGate, OneState, OneEffect\n",
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"from qualtran.bloqs.phase_estimation import TextbookQPE, RectangularWindowState, LPResourceState, KaiserWindowState"
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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": "ae2404c0-b51e-4196-905f-94310abac5fa",
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"metadata": {},
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"outputs": [],
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"source": [
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"def construct_composite_boq(bloq: TextbookQPE) -> CompositeBloq:\n",
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" bb = BloqBuilder()\n",
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" q = bb.add(OneState())\n",
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" phase_reg, q = bb.add(bloq, q=q)\n",
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" bb.add(OneEffect(), q=q)\n",
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" return bb.finalize(phase_reg=phase_reg)\n",
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"\n",
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"def simulate_theta_estimate(bloq: TextbookQPE, n_samples: int) -> float:\n",
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" cbloq = construct_composite_boq(bloq)\n",
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" final_state = cbloq.tensor_contract()\n",
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" samples = cirq.sample_state_vector(final_state, indices=[*range(bloq.m_bits)], repetitions=n_samples)\n",
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" thetas = samples.dot(1 << np.arange(samples.shape[-1] - 1, -1, -1))\n",
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" return thetas\n",
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"\n",
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"def holevo_variance(thetas):\n",
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" mu = np.mean(np.cos(thetas - theta))\n",
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" return 1 / mu**2 - 1"
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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": "e04196ba-4d8c-481a-a498-a0cf1a991fd6",
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"metadata": {},
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"outputs": [],
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"source": [
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"theta = 0.51234\n",
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"unitary = ZPowGate(2 * theta)\n",
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"n_samples = 100_000\n",
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"m = 6\n",
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"x_vals = [x / 2**m for x in range(2**m)]\n",
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"# Textbook QPE\n",
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"qpe_textbook = TextbookQPE(unitary, RectangularWindowState(m))\n",
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"thetas_textbook = simulate_theta_estimate(qpe_textbook, n_samples)\n",
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"# SinState QPE\n",
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"qpe_sinstate = TextbookQPE(unitary, LPResourceState(m))\n",
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"thetas_sinstate = simulate_theta_estimate(qpe_sinstate, n_samples)\n",
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"# Kaiser QPE\n",
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"kaiser_window_state = KaiserWindowState.from_precision_and_delta(3, 1e-2)\n",
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"alpha = kaiser_window_state.alpha\n",
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"assert kaiser_window_state.bitsize == m, f'{kaiser_window_state.bitsize}'\n",
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"qpe_kaiser_state = TextbookQPE(unitary, kaiser_window_state)\n",
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"thetas_kaiser_state = simulate_theta_estimate(qpe_kaiser_state, n_samples)"
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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": "f074f9e0-773c-4076-8461-d99560e25db0",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"\n",
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"plt.rcParams['figure.figsize'] = (20, 10)\n",
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"\n",
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"theta_counts_textbok = np.bincount(thetas_textbook) / n_samples\n",
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"theta_counts_sinstate = np.bincount(thetas_sinstate) / n_samples\n",
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"theta_counts_kaiser = np.bincount(thetas_kaiser_state) / n_samples\n",
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"var_textbook = holevo_variance(thetas_textbook / 2**m)\n",
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"var_sinstate = holevo_variance(thetas_sinstate / 2**m)\n",
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"var_kaiser = holevo_variance(thetas_kaiser_state / 2**m)\n",
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"\n",
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"plt.plot(np.array(x_vals[:len(theta_counts_textbok)]), theta_counts_textbok, label=r\"TextbookQPE; var($\\tilde{\\phi}$)=\"f\"{var_textbook:.2e}\")\n",
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"plt.plot(np.array(x_vals[:len(theta_counts_sinstate)]), theta_counts_sinstate, label=r\"SinStateQPE; var($\\tilde{\\phi}$)=\"f\"{var_sinstate:.2e}\")\n",
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"plt.plot(np.array(x_vals[:len(theta_counts_kaiser)]), theta_counts_kaiser, label=f\"KaiserQPE({alpha=:0.3}); \"r\"var($\\tilde{\\phi}$)=\"f\"{var_kaiser:.2e}\")\n",
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"plt.vlines(theta, 0, 1, linestyles='--', label=f'True Phase $\\phi$={theta}', colors='red')\n",
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"plt.yscale('log', base=10)\n",
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"plt.ylabel(f'Fraction of samples')\n",
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"plt.xlabel(f'{m}-bit approximation of phase measured by running QPE. Should be close to {theta=}')\n",
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"plt.title(f'QPE on ZPowGate(2 * {theta}) using {m=} bit control register and {n_samples} samples.')\n",
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"plt.legend()\n",
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"plt.show()"
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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 (ipykernel)",
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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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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.8"
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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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