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Quantum Information Systems with Q3
This compilation of tutorial documents is intended as an introductory text on quantum computation and as a self-learning guide. It is an attempt to collect some fundamental principles and elementary methods in the field of quantum computation and quantum information and then reorganize them in a compact and integrated form. Through tutorial documents in this compilation, the usage of is also demonstrated.
The Postulates of Quantum Mechanics
It summarizes the fundamental postulates of quantum mechanics and effectively provides a brief review of basic concepts and fundamental principles of quantum mechanics.
Time Evolution of Quantum States
Measurements on Quantum States
Quantum Computation: Overview
It presents and describes elementary quantum gates for universal quantum computation. These are the building blocks of quantum algorithms and quantum communication protocols.
Single-Qubit Gates
Two-Qubit Gates
Multi-Control NOT Gate
Multi-Control Unitary Gates
Universal Quantum Computation
Computational Model of Measurement
Quantum Computation: Models
It explains physical methods and principles to implement elementary quantum gates and introduces different quantum computation schemes.
Measurement-Based Scheme
Quantum Algorithms
It introduces some widely known quantum algorithms to help grasp the idea of the so-called quantum supremacy of quantum algorithms over their classical counterparts.
Quantum Decision Algorithms
Quantum Phase Estimation
Order-Finding and Factorization
Quantum Search Algorithm
Quantum Noise and Decoherence
It introduces mathematical methods including quantum operation and quantum master equation to describe quantum noise and decoherence effects. It also discusses the distance measures for quantum states.
How Quantum Decoherence Occurs
Quantum Master Equation
Distance Measures Between Quantum States
Quantum Error-Correction Codes
It is devoted to quantum error-correction codes through a discussion of the basic principles, procedures, and examples.
The Nine-Qubit Code
Quantum Error-Correction Theorems
Stabilizer Formalism
Stabilizer Codes
Surface Codes
Quantum Information Theory
It introduces quantum information theory. It discusses the entropies of quantum information content and the measures for quantum entanglement degree focusing on quantum entanglement as a valuable physical resource for quantum information processing and quantum communication.
Shannon Entropy
Von Neumann Entropy
Entanglement and Entropy
Appendix
Distance Measures between Quantum States
The Pauli and Clifford Groups
Hadamard Test
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