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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "bbc3afcf", | ||
| "metadata": { | ||
| "cq.autogen": "title_cell" | ||
| }, | ||
| "source": [ | ||
| "# Rz Rotation via Phase Gradient" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "e6ca3000", | ||
| "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": "4d0db53e", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.bloq_doc.md" | ||
| }, | ||
| "source": [ | ||
| "## `RzViaPhaseGradient`\n", | ||
| "Apply a controlled-Rz using a phase gradient state.\n", | ||
| "\n", | ||
| "Implements the following unitary action:\n", | ||
| "\n", | ||
| "$$\n", | ||
| " |\\psi\\rangle \\otimes |x\\rangle \\mapsto \\text{Rz}(4 \\pi x) |\\psi\\rangle \\otimes |x\\rangle\n", | ||
| "$$\n", | ||
| "\n", | ||
| "for every state $|\\psi\\rangle$ and every $x$, or equivalently\n", | ||
| "\n", | ||
| "$$\n", | ||
| " |b\\rangle|x\\rangle \\mapsto |b\\rangle e^{- (-1)^b i x/2} |x\\rangle\n", | ||
| "$$\n", | ||
| "\n", | ||
| "for every $b \\in \\{0, 1\\}$ and every $x$.\n", | ||
| "\n", | ||
| "To apply an $\\text{Rz}(\\theta) = e^{-i Z \\theta/2}$, the angle register $x$ should store $\\theta/(4\\pi)$.\n", | ||
| "\n", | ||
| "#### Parameters\n", | ||
| " - `angle_dtype`: Data type for the `angle_data` register.\n", | ||
| " - `phasegrad_dtype`: Data type for the phase gradient register. \n", | ||
| "\n", | ||
| "#### Registers\n", | ||
| " - `q`: The qubit to apply Rz on.\n", | ||
| " - `angle`: The rotation angle in radians.\n", | ||
| " - `phase_grad`: The phase gradient register of sufficient width. \n", | ||
| "\n", | ||
| "#### References\n", | ||
| " - [Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization](https://arxiv.org/abs/2007.07391). Section II-C: Oracles for phasing by cost function. Appendix A: Addition for controlled rotations.\n" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "88ae8ba0", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.bloq_doc.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.bloqs.rotations import RzViaPhaseGradient" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "f3d5ab59", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.example_instances.md" | ||
| }, | ||
| "source": [ | ||
| "### Example Instances" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "16a874c9", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.rz_via_phase_gradient" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran import QFxp\n", | ||
| "\n", | ||
| "rz_via_phase_gradient = RzViaPhaseGradient(angle_dtype=QFxp(4, 4), phasegrad_dtype=QFxp(4, 4))" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "ca4ac4bc", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.graphical_signature.md" | ||
| }, | ||
| "source": [ | ||
| "#### Graphical Signature" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "92d7b03c", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.graphical_signature.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.drawing import show_bloqs\n", | ||
| "show_bloqs([rz_via_phase_gradient],\n", | ||
| " ['`rz_via_phase_gradient`'])" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "id": "03999011", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.call_graph.md" | ||
| }, | ||
| "source": [ | ||
| "### Call Graph" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": null, | ||
| "id": "d0cc79d3", | ||
| "metadata": { | ||
| "cq.autogen": "RzViaPhaseGradient.call_graph.py" | ||
| }, | ||
| "outputs": [], | ||
| "source": [ | ||
| "from qualtran.resource_counting.generalizers import ignore_split_join\n", | ||
| "rz_via_phase_gradient_g, rz_via_phase_gradient_sigma = rz_via_phase_gradient.call_graph(max_depth=1, generalizer=ignore_split_join)\n", | ||
| "show_call_graph(rz_via_phase_gradient_g)\n", | ||
| "show_counts_sigma(rz_via_phase_gradient_sigma)" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "name": "python" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 5 | ||
| } |
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