Quantum Machine Learning

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Ai Jianhang 2019.11.29 Content

1. Quantum Mechanics 2. Quantum Computing 3. Quantum Computer 4. Quantum Algorithm 5. Quantum Machine Learning Chapter 1

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篇章 Quantum Mechanics Double-slit experiment Quantum Mechanics

Probability wave

Particle Wave Super Position Schrödinger's cat Measurement Problem

• Copenhagen Interpretation • Parallel Universes/High-dimensional projection • And all others Quantum Entanglement Classical Mechanics Quantum Mechanics --- vector in n dimensional complex space n--- Disdingishable states of the system Normalized --- Hamiltonian Schrödinger equation --- Reduced Planck Constant Quantum Mechanics

https://www.reddit.com/r/p hysicsmemes/comments/b 5nksi/is_it_true_that_gravita tional_force_cannot_be/ Chapter 2

Quantum Computing

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篇章 Quantum Computing Quantum computing takes advantage of quantum physics features • superposition • entanglement/ Notations

Dirac Notation/Bra-ket Vector a Vector 0 Inner Product of two vectors and • •

2-dimension space over complex number

Ortho-normal Basis

Projection Operator :

: Projection Operator :

: Qubit Qubit Multiple Qubits and Uniform Superposition Basis of 2 qubit quantum system

Basis of n quit quantum system

Uniform superposition Quantum Gate

Classical Gate Quantum Gate

NOT — single CNOT -- pair AND — pair Hadamard gate -- single OR— pair Pauli-Z gate -- single

Universal logic gates Universal quantum gates NAND/NOR • reversible • unitary Quantum Gate Not gate

Hadamard gate Quantum Gate Pauli- Z gate

CNOT gate Quantum Gate • XOR gate Quantum Gate • CNOT gate maps to Quantum Gate

Chapter 3

Quantum Computers

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篇章 Quantum Computers • Use particles such as electron or photon represent qubit • Quantum Circuit • Silicon Clips • Strong Magnetic • Low temperature Quantum Computers Quantum Computers Quantum Computers

• Dwave/Quantum Annealing • Google/Sycamore Chapter 4

Quantum Algorithm

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篇章 Quantum Algorithm

• Deutsch and Deutsch-Jozsa Algorithm • Grover Algorithm —— Searching Problem • Shor Algorithm —— Factoring Problem • Quantum Annealing Algorithm —— Finding Global Minimum • HHL —— Matrix Inversion and Relevant Problem Deutsch-Jozsa Algorithm Boolean function

is constant or balanced? Classical method : 2 Quantum method:? Deutsch-Jozsa Algorithm If is constant

If is balance Grover Algorithm Grover Algorithm --- Oracle ---

Grover Algorithm • 1 qubit system

Grover Algorithm • Gerneral outline

Grover Algorithm • Subroutine

Grover diffusion operator Grover Algorithm • Rotation

Grover Algorithm • Subroutine

Grover Algorithm • Converge

Grover Algorithm Chapter 5

Quantum Machine Learning

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篇章 Quantum Machine Learning

• To speed up the machine learning algorithm we al- ready have • Design new machine algorithm baesd on the prop- erties of quantum devices • How quantum machine learning will help to chara- cterize and control the quantum computers Quantum machine learning

Linear-algebra based quantum machine learning • Quantum principal component analysis • Quantum support vector machines and kernel methods • Deep quantum learning Quantum machine learning for quantum data Designing and controlling quantum systems What has been left out

• The energy principle involved during building quantum devices in practical such as transistors in silicon chips which operating the quantum gates, also the energy annealing algorithm used • The error-correction/Decohrence • And all others I even haven't noticed Reference

• Biamonte J, Wittek P, Pancotti N, et al. Quantum machine learning[J]. Nature, 2017, 549(7671): 195-202. • Quantum Machine Learning • Introduction to Quantum Computing • Quantum Computing Concepts Thank you for attention