introduction to quantum computing - kursusedcourses.cs.ut.ee/2012/ska/uploads/main/lecture1.pdf ·...

Introduction to Quantum Computing

Einar PiusUniversity of Edinburgh

Tuesday, 17 April 12

Why this Course

• To raise interest in quantum computing

• To show how quantum computers could be useful

• To talk about concepts not found in the textbooks


The Lecturers

Einar Pius

• The guy talking in front of you

• Will give the first lectures. (Introduction)


The Lecturers

Einar Pius

• The guy talking in front of you

• Will give the first lectures. (Introduction)

Vedran Dunjko

• Will join us on the second Week


About the Course

• Course language: English vs Estonian

• Target audience (Computer Scientist vs Physicist)

• We expect basic knowledge of linear algebra

• We do not expect any knowledge of physics

• Basis for the new Quantum Computing course given at the University of Edinburgh next semester


What You Will Learn

• The framework of quantum mechanics [Einar]

• The quantum circuits model [Einar]

• A few quantum algorithms [Einar]

• Quantum depth complexity [Einar]

• The Measurement Based Quantum Computing model [Vedran]

• Universal Blind Quantum Computing [Vedran]


What We Will Not Talk About

• Quantum Information Theory

• Error correction and fault tolerance

• Shor’s algorithm

• Quantum key distribution

• Building quantum computers


Today

• Introduction

• Motivation for quantum computers

• The Stern-Gerlach experiment

• Course structure

• How to pass the course

• Linear algebra

• Dirac notation

• Inner products

• Tensor products

• Operators


Introduction to the Course


Motivation

• Simulating quantum physics (Feynman, 1982)


Motivation


• Solving classically hard computational problems


Motivation



• Factorizing integers


Motivation




• Computing discrete logarithms


Motivation





• Approximating the Jones polynomial


Motivation






• Solving problems faster than on classical computers


Motivation







• Grover’s algorithm


Motivation







• Grover’s algorithm

• Unconditionally secure quantum cloud computing


Quantum Effects(The Stern-Gerlach Experiment)


Timetable

• Quantum mechanics [Wednesday, April 18]

• Quantum cicuits [Thursday, April 19]

• Grover’s algorithm [Friday, April 20]

• Quantum Fourier Transform [Monday, April 23]

• Simulating Clifford circuits [Tuesday, April 24]

• Quantum depth complexity [Wednesday, April 25]

• The Measurement Based Quantum Computing model [Thursday, April 26]

• Universal Blind Quantum Computing [Friday, April 27]

• Lecture chosen by students [Monday, April 30]


Passing the Course

• 40% is given for attendance

• 30% for discussion in the lectures

• 30% for homework

• Homework is given on Monday, April 30

• Answers can be found in text books and/or research papers

• Working in groups is allowed

• Individual answers from everyone


Some Books

• Quantum Computation and Quantum Information (2000) Michael A. Nielsen & Isaac L. Chuang

• An Introduction to Quantum Computing (2007) P. Kaye, R. Laflamme, M. Mosca


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Linear Algebra


the Dirac Notation

• Vector. Also known as a ket.

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the Dirac Notation

• Vector. Also known as a ket.

• Dual vector of . Also known as a bra.

• is the complex conjugate of the complex number

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Operators

• A linear operator between vector spaces and is defined to be any function which is linear in its inputs,

• Linear operators can be represented as matrices.

A : V ! W

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Hermitian Conjugate(Adjoint)

• In matrix representation, the Hermitian conjugate or adjoint of a matrix A is defined as its conjugate transpose:

A† = (AT )⇤


Unitary and Hermitian operators

• Unitary operators

• Hermitian operatorsUU† = I

H = H†


The Tensor Product


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