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Aksbel Book Series

Variational Quantum Algorithms for Optimization

From quantum foundations to real-world optimization applications

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Variational Quantum Algorithms for Optimization 2 contributors · 1 reader

1

Table of contents

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2

3

How to read this book

4

Introduction

1

variational quantum algorithms

5

Chapter 1: Why Quantum Optimization Matters

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Chapter 2: Mathematical Foundations for Optimization

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Chapter 3: Classical Optimization Methods You Must Know

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Chapter 4: Quantum Computing from First Principles

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Chapter 5: From Quantum Circuits to Quantum Algorithms

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Chapter 6: The Variational Algorithm Idea

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Chapter 7: Parameterized Quantum Circuits and Ansatz Design

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Chapter 8: Measuring Cost Functions on Quantum Devices

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Chapter 9: Classical Optimizers for Variational Quantum Algorithms

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Chapter 10: The Variational Quantum Eigensolver

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Chapter 11: Optimization as an Ising or QUBO Problem

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Chapter 12: The Quantum Approximate Optimization Algorithm

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Chapter 13: QAOA for Canonical Problems

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Chapter 14: Beyond Standard QAOA

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Chapter 15: Quantum Annealing and Its Relationship to VQAs

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Chapter 16: Noise, Errors, and Hardware Constraints

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Chapter 17: Barren Plateaus and Trainability

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Chapter 18: Benchmarking Quantum Optimization Honestly

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Chapter 19: Software Tools and Practical Workflows

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Chapter 20: Real-Life Application Areas

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Chapter 21: Case Study: Portfolio Optimization

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Chapter 22: Case Study: Routing and Scheduling

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Chapter 23: Research Frontiers and Open Problems

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Chapter 24: Building Your Own Quantum Optimization Project

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Pemuliaan Genetik Kentang 1 contributor · 1 reader

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Pendahuluan

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Bab 1: Mengapa Kentang Sulit dan Menarik untuk Dimuliakan

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Bab 2: Dasar Botani dan Siklus Hidup Kentang

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Bab 3: Prinsip Genetika untuk Pemulia Pemula

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Bab 4: Keunikan Genetika Kentang: Tetraploid, Heterozigot, dan Klonal

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Bab 5: Menentukan Tujuan Pemuliaan yang Jelas

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Bab 6: Sumber Keragaman Genetik Kentang

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Bab 7: Karakter Penting dalam Pemuliaan Kentang

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Bab 8: Ketahanan Penyakit dan Hama

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Bab 9: Adaptasi Lingkungan dan Ketahanan Stres

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Bab 10: Persilangan dan Produksi Keturunan

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Bab 11: Seleksi Klonal dari Generasi Awal hingga Calon Varietas

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Bab 12: Pemuliaan Kentang Diploid dan True Potato Seed

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Bab 13: Kultur Jaringan dan Perbanyakan Bebas Penyakit

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Bab 14: Marka Molekuler dan Seleksi Berbantuan DNA

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Bab 15: Genomik, GWAS, dan Seleksi Genomik

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Bab 16: Bioteknologi dan Penyuntingan Gen dengan Tanggung Jawab

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Bab 17: Desain Percobaan Lapang dan Uji Multilokasi

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Bab 18: Data Pemuliaan dan Keputusan Seleksi

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Bab 19: Mutu Benih Kentang dan Sistem Sertifikasi

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Bab 20: Perlindungan Varietas, Lisensi, dan Strategi Komersialisasi Benih

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Bab 21: Etika, Akses Petani, dan Keberlanjutan

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Bab 22: Membangun Program Pemuliaan Kentang dari Nol

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Pemuliaan Genetik Kentang 1 contributor · 1 reader

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Pendahuluan

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Bab 1: Peta Besar Pemuliaan Kentang

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Bab 2: Biologi Kentang sebagai Tanaman Pemuliaan

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Bab 3: Dasar Genetika untuk Pemulia Pemula

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Bab 4: Keunikan Genetik Kentang Tetraploid

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Bab 5: Plasma Nutfah dan Keragaman Genetik Kentang

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Bab 6: Menentukan Target Pemuliaan

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Bab 7: Sifat Agronomis Penting

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Bab 8: Kualitas Umbi dan Kebutuhan Industri

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Bab 9: Penyakit dan Hama Utama Kentang

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Bab 10: Genetika Ketahanan Penyakit

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Bab 11: Persilangan dalam Pemuliaan Kentang

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Bab 12: Seleksi Klonal dari Biji hingga Kandidat Varietas

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Bab 13: Desain Percobaan Lapang

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Bab 14: Statistik Praktis untuk Pemuliaan Kentang

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Bab 15: Penanda Molekuler dan Seleksi Berbantuan Marker

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Bab 16: Genomik dan Pemuliaan Modern

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Bab 17: Pemuliaan Diploid dan True Potato Seed

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Bab 18: Kultur Jaringan dan Perbanyakan Benih Sehat

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Bab 19: Sistem Produksi Benih Kentang

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Bab 20: Sertifikasi, Regulasi, dan Pelepasan Varietas

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Bab 21: Perlindungan Varietas dan Hak Kekayaan Intelektual

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Bab 22: Strategi Komersialisasi Benih yang Berkelanjutan

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Bab 23: Etika, Keamanan Hayati, dan Dampak Sosial

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Bab 24: Merancang Program Pemuliaan Kentang Anda Sendiri

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Masakan Tradisional Jawa Tengah 2 contributors · 1 reader

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Bab 1: Peta Rasa Jawa Tengah

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Bab 2: Sejarah, Budaya, dan Etika Makan Jawa

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Bab 3: Dapur Dasar: Alat, Kebersihan, dan Keselamatan

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Bab 4: Bahan Pokok dan Cara Memilihnya

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Bab 5: Rempah, Bumbu, dan Aromatik Jawa Tengah

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Bab 6: Teknik Membuat Bumbu Dasar

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Bab 7: Teknik Memasak Utama dalam Masakan Jawa Tengah

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Bab 8: Nasi, Lontong, dan Hidangan Beras

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Bab 9: Sayur Berkuah dan Masakan Harian

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Bab 10: Tempe, Tahu, dan Olahan Kedelai

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Bab 11: Ayam, Telur, dan Hidangan Ungkep

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Bab 12: Daging, Jeroan, dan Hidangan Istimewa

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Bab 13: Ikan, Seafood, dan Masakan Pesisir

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Bab 14: Sambal, Lalapan, dan Pelengkap

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Bab 15: Ikon Kuliner Kota dan Daerah

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Bab 16: Jajan Pasar dan Kudapan Tradisional

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Bab 17: Minuman Tradisional dan Penyegar

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Bab 18: Merancang Menu Jawa Tengah

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Bab 19: Menyesuaikan Resep untuk Kesehatan dan Kebutuhan Modern

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Bab 20: Belanja, Persiapan, dan Manajemen Waktu

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Bab 21: Penyajian, Daun Pisang, dan Rasa Estetika Jawa

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Bab 22: Latihan Proyek: Dari Resep ke Meja Makan

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Dapur Jawa Tengah 2 contributors · 1 reader

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Pendahuluan

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Bab 1: Mengenal Rasa dan Budaya Masakan Jawa Tengah

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Bab 2: Bahan Pokok Dapur Jawa Tengah

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Bab 3: Dasar Bumbu: Mengiris, Mengulek, dan Menumis

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Bab 4: Kaldu, Santan, dan Keseimbangan Rasa

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Bab 5: Nasi, Lontong, dan Hidangan Pokok

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Bab 6: Gudeg dan Krecek: Ikon Masakan Jawa Tengah

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Bab 7: Soto, Sup, dan Masakan Berkuah

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Bab 8: Olahan Ayam dan Telur Tradisional

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Bab 9: Olahan Daging, Jeroan, dan Sate

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Bab 10: Ikan, Seafood, dan Masakan Sungai-Pantai

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Bab 11: Tempe, Tahu, dan Lauk Nabati

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Bab 12: Sayur Tradisional dan Hidangan Rumahan

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Bab 13: Sambal, Lalapan, dan Pelengkap Wajib

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Bab 14: Jajan Pasar Jawa Tengah

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Bab 15: Hidangan Manis, Wedang, dan Minuman Tradisional

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Bab 16: Teknik Memasak untuk Dapur Rumah Modern

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Bab 17: Menyusun Menu Harian, Selamatan, dan Hidangan Tamu

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Bab 18: Belanja, Penyimpanan, dan Keamanan Pangan

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Bab 19: Membaca, Menguji, dan Mengembangkan Resep

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Bab 20: Proyek Akhir: Memasak Satu Set Menu Jawa Tengah

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Meracik Parfum Spray dari Minyak Atsiri 2 contributors · 1 reader

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Bab 1: Dunia Parfum Spray Berbasis Minyak Atsiri

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Dalam buku ini, kita akan fokus pada parfum spray berbasis minyak atsiri. Artinya, sumber aroma utama yang kita pelajari adalah minyak atsiri dari tumbuhan, tetapi bentuk akhirn...

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Bab 2: Dasar Kimia Aroma untuk Pemula

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Bab 3: Mengenal Minyak Atsiri dan Kualitas Bahan

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Bab 4: Keluarga Aroma dan Karakter Utama

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Bab 5: Top, Middle, dan Base Notes

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Bab 6: Keamanan Kulit, Dosis, dan Batas Penggunaan

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Bab 7: Pelarut, Alkohol, dan Struktur Parfum Spray

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Bab 8: Alat, Satuan, dan Cara Mengukur Campuran

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Bab 9: Rasio Dasar Pencampuran Aroma

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Bab 10: Jenis Pencampuran yang Lazim

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Bab 11: Membuat Accord Sederhana

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Bab 12: Proses Meracik dari Ide Menjadi Formula

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Bab 13: Maserasi, Aging, dan Penyaringan

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Bab 14: Evaluasi Aroma dan Perbaikan Formula

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Bab 15: Profil Minyak Atsiri yang Sering Dipakai

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Bab 16: Membuat Parfum Spray 10 ml, 30 ml, dan 50 ml

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Bab 17: 20 Resep Praktik Parfum Spray di Rumah

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Bab 18: Troubleshooting dan Kebiasaan Peracik yang Baik

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Plant Tissue Culture for Farmers 2 contributors · 1 reader

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Table of contents

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How to read this book

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Introduction

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Chapter 1: What Plant Tissue Culture Can and Cannot Do

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Chapter 2: The Biology Behind Tissue Culture

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Chapter 3: Setting Up a Small Low-Cost Culture Space

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Chapter 4: Tools, Containers, and Materials

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Chapter 5: Sterility, Contamination, and Farmer-Level Lab Discipline

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Chapter 6: Media Basics: Nutrients, Sugar, Gelling Agents, and pH

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Chapter 7: Plant Growth Regulators Made Understandable

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Chapter 8: Preparing Explants from Healthy Mother Plants

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Chapter 9: Surface Sterilization Protocols

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Chapter 10: First Cultures: Starting Without Overcomplication

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Chapter 11: Shoot Multiplication Projects

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Chapter 12: Rooting and Plantlet Development

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Chapter 13: Hardening and Acclimatization in the Nursery

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Chapter 14: 50 Beginner Tissue Culture Projects Map

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Chapter 15: Food Crop Projects 1–10

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Chapter 16: Herb, Spice, and Medicinal Plant Projects 11–20

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Chapter 17: Vegetable and Seedling Support Projects 21–30

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Chapter 18: Ornamental Plant Projects 31–40

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Chapter 19: Tree, Plantation, and Advanced Crop Projects 41–50

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Chapter 20: Troubleshooting Culture Problems

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Chapter 21: Records, Data, and Simple Production Math

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Chapter 22: Disease-Free Planting Material and Quality Control

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Chapter 23: Safety, Ethics, Regulations, and Responsible Selling

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Chapter 24: Building a Small Tissue Culture Enterprise

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Lulus Interview Visa K-STAR dengan Bahasa Korea Dasar 1 contributor · 0 readers

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Pendahuluan

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Bab 1: Memahami Tujuan Interview Visa K-STAR

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Bab 2: Strategi Belajar Cepat untuk Pemula Nol Bahasa Korea

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Bab 3: Hangeul Super Dasar untuk Membaca Nama dan Dokumen

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Bab 4: Pengucapan Korea yang Aman untuk Interview

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Bab 5: Etika Sopan Santun dalam Wawancara Korea

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Bab 6: Kalimat Bertahan Hidup Saat Tidak Paham

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Bab 7: Memperkenalkan Diri dalam Bahasa Korea

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Bab 8: Menjelaskan Tujuan Mengajukan Visa K-STAR

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Bab 9: Menjawab Pertanyaan tentang Studi dan Latar Belakang Akademik

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Bab 10: Menjelaskan Rencana Kegiatan di Korea

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Bab 11: Menjawab Pertanyaan tentang Keuangan dan Sponsor

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Bab 12: Menunjukkan Niat Kembali ke Indonesia

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Bab 13: Menjawab Pertanyaan tentang Akomodasi, Kontak, dan Keamanan

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Bab 14: Kosakata Inti Interview Visa Korea

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Bab 15: Pola Jawaban Korea yang Bisa Diadaptasi

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Bab 16: Pertanyaan Interview Paling Umum dan Jawaban Model

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Bab 17: Pertanyaan Sulit dan Cara Menjawab Tanpa Terjebak

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Bab 18: Menyelaraskan Jawaban dengan Dokumen

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Bab 19: Latihan Mendengar Pertanyaan Korea

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Bab 20: Simulasi Interview Bertahap

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Bab 21: Skrip Pribadi Interview Visa K-STAR

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Bab 22: Rencana Latihan 7 Hari Sebelum Interview

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Bab 23: Hari-H Interview: Dari Masuk Ruangan sampai Selesai

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Bab 24: Checklist Akhir dan Bank Jawaban Cepat

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Naimark Dilation from First Principles 1 contributor · 0 readers

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Table of contents

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2

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How to read this book

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Introduction

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Chapter 1: The Measurement Problem in Quantum Information

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Chapter 2: Linear Algebra for Quantum Theory

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Chapter 3: Hilbert Spaces and Operators

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Chapter 4: Quantum States

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Chapter 5: Projective Measurements

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Chapter 6: From Projective Measurements to POVMs

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Chapter 7: Probability, Positivity, and the Born Rule for POVMs

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Chapter 8: Ancillas and Enlarged Quantum Systems

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Chapter 9: Isometries, Embeddings, and Dilations

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Chapter 10: Statement of Naimark's Dilation Theorem

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Chapter 11: The Finite-Dimensional Proof

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Chapter 12: Understanding the Construction

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Chapter 13: Minimal Dilations and Uniqueness

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Chapter 14: Measurement Operators and Instruments

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Chapter 15: Naimark Dilation via Unitary Interaction

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Chapter 16: Relation to Stinespring Dilation

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Chapter 17: Examples of POVM Dilations

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Chapter 18: Quantum State Discrimination

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Chapter 19: Quantum Communication and Information Extraction

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Chapter 20: Quantum Cryptography and Security

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Chapter 21: Quantum Tomography and Experimental Measurement

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Chapter 22: Infinite-Dimensional and Measure-Theoretic Outlook

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Chapter 23: Common Pitfalls and Proof Techniques

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Chapter 24: Capstone: Building and Using a Naimark Dilation

29

Bertani Cabai Efektif dan Menguntungkan 1 contributor · 1 reader

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Pendahuluan

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Bab 1: Memahami Usaha Tani Cabai

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Bab 2: Mengenal Tanaman Cabai dari Dasar

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Bab 3: Memilih Jenis dan Varietas Cabai yang Tepat

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Bab 4: Membaca Pasar dan Merancang Target Keuntungan

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Bab 5: Memilih Lokasi dan Menilai Kesesuaian Lahan

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Bab 6: Menyiapkan Tanah yang Subur dan Sehat

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Bab 7: Perencanaan Modal, Biaya, dan Jadwal Tanam

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Bab 8: Persemaian Benih yang Kuat

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Bab 9: Teknik Tanam yang Benar

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Bab 10: Irigasi dan Pengelolaan Air

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Bab 11: Pemupukan Berimbang untuk Hasil Tinggi

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Bab 12: Perawatan Harian Tanaman Cabai

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Bab 13: Mengendalikan Gulma, Hama, dan Penyakit Secara Terpadu

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Bab 14: Hama Utama Cabai dan Cara Mengatasinya

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Bab 15: Penyakit Utama Cabai dan Pencegahannya

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Bab 16: Mengelola Fase Berbunga dan Berbuah

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Bab 17: Panen Cabai yang Tepat dan Berkualitas

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Bab 18: Pascapanen, Penyimpanan, dan Pengemasan

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Bab 19: Strategi Menjual Cabai dengan Harga Lebih Baik

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Bab 20: Menghitung Laba, Evaluasi, dan Pengembangan Usaha

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Grover's Algorithm from First Principles 1 contributor · 0 readers

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Table of contents

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2

3

How to read this book

4

Introduction

5

Chapter 1: Why Quantum Search Matters

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Chapter 2: Complex Numbers, Vectors, and Inner Products

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Chapter 3: Qubits and Quantum States

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Chapter 4: Measurement and Probability

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Chapter 5: Quantum Gates and Circuits

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Chapter 6: Reversible Computation and Oracles

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Chapter 7: The Unstructured Search Problem

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Chapter 8: Phase Kickback and Phase Oracles

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Chapter 9: Creating the Uniform Superposition

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Chapter 10: The Diffusion Operator

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Chapter 11: One Full Grover Iteration

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Chapter 12: The Geometry of Amplitude Amplification

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Chapter 13: How Many Iterations Are Needed

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Chapter 14: Complexity and the Quadratic Speedup

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Chapter 15: Multiple Solutions and Unknown Solution Counts

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Chapter 16: Building Practical Grover Oracles

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Chapter 17: Worked Example: Searching a Small Space

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Chapter 18: Using Grover in Quantum Programming Frameworks

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Chapter 19: Noise, Hardware Limits, and Real Devices

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Chapter 20: Amplitude Amplification Beyond Search

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Chapter 21: Applications and Misapplications

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Chapter 22: From Grover to Future Quantum Algorithms

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Shor's Algorithm from First Principles 1 contributor · 0 readers

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Table of contents

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2

3

How to read this book

4

Introduction

5

Chapter 1: The Problem Shor Solves

6

Chapter 2: Classical Computation, Complexity, and Reversibility

7

Chapter 3: Qubits from Linear Algebra

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Chapter 4: Quantum Gates and Circuits

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Chapter 5: Superposition, Interference, and Entanglement

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Chapter 6: Number Theory for Factoring

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Chapter 7: From Factoring to Order Finding

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Chapter 8: Periodic Functions and Hidden Structure

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Chapter 9: The Quantum Fourier Transform

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Chapter 10: Building the QFT Circuit

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Chapter 11: Quantum Phase Estimation

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Chapter 12: Modular Exponentiation as a Quantum Operation

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Chapter 13: The Full Shor Factoring Algorithm

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Chapter 14: Why the Measurement Reveals the Period

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Chapter 15: Continued Fractions and Classical Postprocessing

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Chapter 16: Worked Examples by Hand

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Chapter 17: Correctness, Runtime, and Success Probability

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Chapter 18: Shor's Algorithm for Discrete Logarithms

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Chapter 19: The Hidden Subgroup Perspective

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Chapter 20: Applying the Principles to New Problems

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Chapter 21: Limits, Noise, and Real Hardware

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Chapter 22: Cryptographic Consequences

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Chapter 23: Implementing and Simulating Shor's Algorithm

28

Chapter 24: Mastery Map and Further Directions

29

Nahwu Sharaf Ceria 1 contributor · 0 readers

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Pendahuluan

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Bab 1: Mengenal Bahasa Arab dan Huruf-Hurufnya

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Bab 2: Kata dalam Bahasa Arab

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Bab 3: Isim: Nama, Benda, dan Sifat

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Bab 4: Fi'il: Kata Kerja dan Waktu

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Bab 5: Dasar Sharaf: Perubahan Bentuk Kata

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Bab 6: Kalimat Ismiyah: Mubtada dan Khabar

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Bab 7: Kalimat Fi'liyah: Fi'il dan Fa'il

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Bab 8: Tanda Akhir Kata: Dhammah, Fathah, dan Kasrah

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Bab 9: Membaca dan Membuat Kalimat Arab Sederhana

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Membaca Hanacaraka 1 contributor · 0 readers

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Pendahuluan

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Bab 1: Peta Aksara Jawa dan Cara Kerjanya

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Bab 2: Aksara Nglegena: Dua Puluh Huruf Dasar

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Bab 3: Sandhangan Swara dan Pengubah Bunyi

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Bab 4: Pasangan dan Cara Mematikan Vokal

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Bab 5: Sandhangan Panyigeg, Wyanjana, dan Gugus Konsonan

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Bab 6: Angka, Tanda Baca, dan Tata Tulis Teks Jawa

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Bab 7: Aksara Murda, Swara, dan Rekan

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Bab 8: Strategi Membaca Lancar dari Kata ke Paragraf

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Bab 9: Membaca Teks Asli dan Alih Aksara

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Membaca Hangeul dari Nol 1 contributor · 0 readers

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Bab 1: Cara Kerja Hangeul

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Bab 2: Vokal Dasar dan Arah Penulisan

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Bab 3: Konsonan Dasar dan Bunyi Awal

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Bab 4: Membentuk dan Membaca Suku Kata

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Bab 5: Konsonan Akhir Batchim

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Bab 6: Vokal Gabungan dan Diftong

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Bab 7: Konsonan Ganda dan Konsonan Aspirasi

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Bab 8: Aturan Pengucapan Saat Kata Dibaca Bersambung

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Bab 9: Latihan Membaca Kata, Nama, dan Kalimat Pemula

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Bab 10: Dari Mengeja ke Membaca Lancar

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Aku Tumbuh Hebat 1 contributor · 1 reader

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Bab 1: Aku Sedang Tumbuh

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Bab 2: Tubuhku Bisa Banyak Hal

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Bab 3: Otakku Suka Belajar

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Bab 4: Aku Punya Banyak Perasaan

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Bab 5: Saat Perasaan Besar Datang

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Bab 6: Aku dan Orang Lain

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Bab 7: Bermain, Berbagi, dan Berteman

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Bab 8: Aku Bisa Mencoba Lagi

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Bab 9: Aku Aman dan Disayang

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Grammar TOEFL Terarah 1 contributor · 1 reader

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Bab 1: Peta Grammar TOEFL dan Cara Membaca Soal

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Bab 2: Kerangka Kalimat Bahasa Inggris

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Bab 3: Subject–Verb Agreement dan Bentuk Kata Kerja

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Bab 4: Noun, Pronoun, Article, dan Parallel Form

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Bab 5: Adjective, Adverb, Comparison, dan Word Form

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Bab 6: Gerund, Infinitive, Participle, dan Reduced Clause

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Bab 7: Clause Kompleks: Noun, Adjective, dan Adverb Clause

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Bab 8: Inversion, Passive Voice, dan Struktur Akademik Lanjutan

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Bab 9: Strategi Error Recognition dan Latihan Simulasi

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Quantum Control in Action 1 contributor · 0 readers

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Table of contents

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2

3

How to read this book

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Introduction

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Chapter 1: Why Quantum Control Matters

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Chapter 2: Quantum Mechanics Needed for Control

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Chapter 3: Dynamics, Pulses, and Steering Quantum Systems

8

Chapter 4: Controllability and the Limits of Control

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Chapter 5: Open Quantum Systems and Decoherence

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Chapter 6: Optimal Quantum Control

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Chapter 7: Feedback, Measurement, and Adaptive Control

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Chapter 8: Applications in Quantum Technologies

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Chapter 9: Applications in Chemistry, Materials, and Nanoscience

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Chapter 10: Designing a Quantum Control Project

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Quantum Circuits from First Principles 1 contributor · 0 readers

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Table of contents

1

2

3

How to read this book

4

Introduction

5

Chapter 1: Qubits, States, and Measurement

6

Chapter 2: Single-Qubit Gates and Circuit Notation

7

Chapter 3: Multi-Qubit Systems and Entanglement

8

Chapter 4: Controlled Gates and Universal Circuit Building Blocks

9

Chapter 5: Reading and Analyzing Quantum Circuits

10

Chapter 6: Core Quantum Circuit Patterns

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Chapter 7: From Circuits to Algorithms

12

Chapter 8: Noise, Measurement, and Real Hardware Constraints

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Chapter 9: Designing, Simulating, and Testing Your Own Circuits

14

Scrodinger Equation 1 contributor · 0 readers

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The Schrödinger equation

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wavefunction

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Born Interpretation

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$\Psi^*(\mathbf{r}, t)\Psi(\mathbf{r}, t)$:

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$$|\Psi|^2 = \Psi^* \Psi = (a - bi)(a + bi) = a^2 + abi - abi - b^2i^2$$

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$$|\Psi|^2 = \Psi^* \Psi = (a - bi)(a + bi) = a^2 + abi - abi - b^2i^2$$

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($\sqrt{-1}$)

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Untitled document

Oracle in Quantum Computing — Detailed Explanation 1 contributor · 0 readers

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Oracle in Quantum Computing — Detailed Explanation

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\[ U_f^2 = I \]

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\[ O\left(\sqrt{\frac{N}{M}}\right) \]

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AI explanation: \[ O\left(\sqrt{\frac{N}{M}}\right) \]

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AI explanation: \[ O(\sqrt{N}) \]

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Two Flavors of the Equation

[QIT 002] State Distinguishability and Measurement Theorems 1 contributor · 0 readers

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Helstrom Theorem

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Holevo Bound

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Fuchs-van de Graaf Inequalities

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Contractivity of Trace Distance

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Monotonicity of Fidelity

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Gentle Measurement Lemma

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Quantum Neyman-Pearson Lemma

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Quantum Stein’s Lemma

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Quantum Chernoff Bound

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Pretty-Good Measurement Bounds

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Accessible Information Bound

[QIT 001] Mathematical Representation Theorems 1 contributor · 0 readers

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Spectral Theorem

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Schmidt Decomposition

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Purification Theorem

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Uniqueness of Purification

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Uhlmann’s Theorem

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Naimark Dilation Theorem

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Stinespring Dilation Theorem

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Kraus Representation Theorem

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Choi-Jamiołkowski Isomorphism

10

Choi’s Complete-Positivity Criterion

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Lindblad-Gorini-Kossakowski-Sudarshan Theorem

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Unitary Freedom of Kraus Representations

LEAN Programming Language 1 contributor · 0 readers

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Lean Programming Language

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The tactic rfl means reflexivity

Quantum clock synchronization (QCS) 1 contributor · 0 readers

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Quantum Clock Synchronization from First Principles

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Replacing a Theoretical Probability by an Empirical Estimate

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Replacing a Theoretical Probability by an Empirical Estimate

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Quantum Einstein Synchronization

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Quantum Eddington Slow-Clock Transport

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What It Means for a Qubit to Tick

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AI explanation: $e^{-i\omega t}$

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\[ U(t)=e^{-iHt/\hbar}. \]

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\[ e^{-iHt/\hbar} = I-\frac{iHt}{\hbar} +\frac{1}{2!}\left(-\frac{iHt}{\hbar}\right)^2 +\frac{1}{3!}\left(-\frac{iHt}{\hbar}\right)^3+\cdots. \]

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