Quantum Amplitude Amplification

An interactive visual survey of amplitude amplification, from Grover's search to modern exact, fixed-point, oblivious, distributed, and QSVT-based frameworks.

Interactive site  |  Detailed survey  |  ampamp documentation

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What This Is

Quantum amplitude amplification is often introduced through dense linear algebra: reflections, phase oracles, diffusion operators, eigenphases, and success amplitudes. This project turns that machinery into an interactive visual language.

The site is designed as a bridge between three layers:

Layer	Purpose
Intuition	Build a geometric feel for amplitudes, rotations, overshooting, damping, and exact convergence.
Survey	Connect each visualization to the historical and technical development of amplitude amplification.
Implementation	Point learners toward the companion ampamp library for practical quantum amplitude amplification workflows.

The result is not just a Grover visualizer. It is a guided map of the amplitude amplification family tree.

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Quick Links

Resource	Link
Interactive visualizer	https://quantumamplification.github.io/QuantumAmplitudeAmplification/
Detailed survey	https://zenodo.org/records/20054981
ampamp library docs	https://quantumamplification.github.io/ampamp/
Glossary	https://quantumamplification.github.io/QuantumAmplitudeAmplification/glossary

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Why It Matters

Amplitude amplification is the engine behind many quantum speedups. It starts with a simple idea: increase the probability of measuring a desired outcome while suppressing the rest. But the modern landscape is much richer than the basic Grover loop.

This visualizer helps answer questions like:

• Why does standard Grover amplification overshoot?
• How do exact and fixed-point methods avoid missing the target?
• What changes when the amplified operation is hidden inside a subroutine?
• How does amplitude estimation turn a quantum probability into a number?
• How can amplification be distributed across smaller quantum processors?
• Why does QSVT act like a unifying polynomial framework?

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Algorithm Map

Module	Route	Core Idea
Grover's Algorithm	/grover	The original quadratic search speedup through oracle and diffusion reflections.
Exact Amplitude Amplification	/eqaa	Phase adjustment that lands exactly on the target state.
Fixed-Point Amplitude Amplification	/fpaa	Monotonic amplification that avoids the "souffle problem" of overshooting.
Amplitude Estimation	/ae	Converts amplified success probability into a digital estimate.
Oblivious Amplitude Amplification	/oblivious	Amplifies the success of a subroutine without inspecting its internal state.
Fixed-Point Oblivious QA	/foqa	Combines oblivious amplification with fixed-point convergence.
Controlled QAA	/cqaa	Uses controlled amplification structure to transform detection into finding.
Distributed QAA	/dqaa	Splits search across smaller quantum processors while preserving speedup intuition.
Distributed Exact QAAA	/deqaaa	Performs exact distributed amplification over a multi-node quantum network.
QSVT	/qsvt	Reframes amplification as polynomial transformation of singular values.
Glossary	/glossary	Defines the recurring language used across the visual explanations.

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Experience Design

The site is built around a repeated learning rhythm:

1. Read a short conceptual step.
2. Watch the associated state, register, or network visualization respond.
3. Move through the algorithm one reflection, phase shift, or amplification stage at a time.
4. Jump to the detailed survey for mathematical depth.
5. Jump to the ampamp docs when you are ready to use the library.

The interface favors quiet, high-contrast visuals, mathematical notation, and compact controls. Each section uses the same core vocabulary so learners can compare algorithms rather than relearn the UI.

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Feature Highlights

• Interactive algorithm walkthroughs: Step through each method as a sequence of visual transformations.
• Unified geometric framing: See amplitude amplification as rotations, reflections, damping, and convergence.
• Inline math rendering: KaTeX keeps equations readable without overwhelming the interface.
• Glossary-linked explanations: Important terms are introduced in context and explained without leaving the flow.
• Resource navigation: Every major page links to the detailed survey and the ampamp library documentation.
• Static export: The app is configured for GitHub Pages deployment.
• Offline-safe production build: The project uses a system font stack, so builds do not fetch Google Fonts.

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Tech Stack

Area	Technology
Framework	Next.js App Router
Language	TypeScript
UI	React
Styling	Tailwind CSS
Animation	Framer Motion
Math rendering	KaTeX via react-katex
Icons	Lucide React
Theme	next-themes
Deployment target	Static export for GitHub Pages

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Local Development

Install dependencies:

npm install

Start the development server:

npm run dev

Build the production export:

npm run build

Run TypeScript checks:

npx tsc --noEmit

The project uses:

basePath: "/QuantumAmplitudeAmplification"

So when running exported or deployed pages, routes live under that GitHub Pages path.

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Project Structure

src/
  app/
    page.tsx              Home page and algorithm grid
    ae/                   Amplitude Estimation route
    cqaa/                 Controlled QAA route
    deqaaa/               Distributed Exact QAAA route
    dqaa/                 Distributed QAA route
    eqaa/                 Exact AA route
    foqa/                 Fixed-Point Oblivious QA route
    fpaa/                 Fixed-Point AA route
    glossary/             Shared terminology route
    grover/               Grover route
    oblivious/            Oblivious AA route
    qsvt/                 QSVT route
    vtaa/                 Variable-Time AA route
  components/
    ae/                   Amplitude Estimation panels and visualization
    cqaa/                 Controlled QAA panels and visualization
    deqaaa/               Distributed Exact QAAA panels and visualization
    dqaa/                 Distributed QAA panels and visualization
    eqaa/                 Exact AA panels and visualization
    foqa/                 FOQA panels and visualization
    fpaa/                 FPAA panels and visualization
    oblivious/            OAA panels and visualization
    qsvt/                 QSVT panels and visualization
    vtaa/                 VTAA panels and visualization
    ResourceLinks.tsx     Shared survey and ampamp documentation links
  lib/
    glossary.ts           Shared glossary content
    links.ts              Canonical external resource URLs

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Companion Library: ampamp

This visualizer explains the concepts. The companion ampamp documentation shows how to put amplitude amplification ideas to work in code.

Use the docs when you want to:

• Move from visual intuition to implementation.
• Explore reusable amplitude amplification primitives.
• Connect the survey's algorithmic variants to practical workflows.
• Build experiments around Grover-style amplification, amplitude estimation, and related techniques.

Library documentation: https://quantumamplification.github.io/ampamp/

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Survey Reference

The detailed survey provides the mathematical and historical foundation behind the visual modules:

https://zenodo.org/records/20054981

Use it for proofs, formal definitions, citations, and deeper comparisons between the algorithms.

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Authors

• Mithilesh Kumar
• Varun Daiya
• Yusuf Tahir

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Build Notes

This repository is configured for static export:

import type { NextConfig } from "next";

const nextConfig: NextConfig = {
  output: "export",
  basePath: "/QuantumAmplitudeAmplification",
  trailingSlash: true,
  turbopack: {
    root: __dirname,
  },
  images: {
    unoptimized: true,
  },
};

export default nextConfig;

The app avoids build-time font downloads, which keeps CI and GitHub Pages builds more reliable. Turbopack root inference is pinned in next.config.ts so the build resolves this repository as the project root even if parent directories contain other lockfiles.

GitHub Pages deployment is handled by .github/workflows/deploy-pages.yml. The workflow installs dependencies with npm ci, runs npm run build, preserves .nojekyll, uploads the generated out/ directory, and deploys it through the official Pages artifact flow.

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License

No open-source license file is currently included. Please contact the authors before reusing or redistributing the source outside the survey project.