Problems & Solutions in Quantum Computing & Quantum Information

Description:

Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems.

All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy, quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and KerrHamilton operator. The topics range in difficulty from elementary to advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given.

Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.

 

 Table of Contents:

• Finite-Dimensional Hilbert Spaces:
• Qubits
• Kronecker Product and Tensor Product
• Matrix Properties
• Density Operators
• Partial Trace
• Unitary Transforms and Quantum Gates
• Measurement
• Entanglement
• Teleportation
• Cloning
• Quantum Algorithms
• Quantum Error Correction
• Quantum Cryptography
• Infinite-Dimensional Hilbert Spaces:
• Harmonic Oscillator and Bose Operators
• Coherent States
• Squeezed States
• Entanglement
• Teleportation
• Swapping and Cloning
• Hamilton Operators

描述：
量子計算和量子信息是物理學中增長最快、最令人興奮的兩個研究領域之一。利用量子力學的非局部行為在隨機多項式時間內因式分解整數的可能性增加了對此的新興趣。這本寶貴的書提供了量子計算和量子信息中的一系列問題以及詳細的解答。它分為兩部分：第一部分考慮有限維系統，而第二部分則處理無限維系統。

所有重要的概念和主題都包含在內，例如量子門和量子電路、纏結、傳輸、貝爾態、貝爾不等式、施密特分解、量子傅立葉變換、魔術門、馮·諾依曼熵、量子密碼學、量子錯誤修正、相干態、擠壓態、POVM測量、分束器和KerrHamilton算子。這些主題的難度從初級到高級不等。幾乎所有的問題都有詳細解答，其中大部分都是自成一體的。所有相關的定義都給出了。

學生可以從這本書中學習到解決問題所需的重要原則和策略。教師會發現它作為補充材料很有用，因為重要的概念和技術是通過問題來發展的。它也可以用作線性和多線性代數或矩陣理論的教材或補充材料。

目錄：
有限維希爾伯特空間：
- 量子位
- 克羅內克乘積和張量乘積
- 矩陣性質
- 密度算子
- 偏迹
- 單位變換和量子門
- 測量
- 纏結
- 傳輸
- 克隆
- 量子算法
- 量子錯誤修正
- 量子密碼學

無限維希爾伯特空間：
- 調和振子和玻色算子
- 相干態
- 擠壓態
- 纏結
- 傳輸
- 交換和克隆
- 哈密頓算子