- 52 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Quantum Computing: An Overview for non-specialists' - helena

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Plan of lecturesPlan of lectures

Financial supports from Kinki Univ., ### Quantum Computing:An Overviewfor non-specialists

MEXT and JSPS

Mikio Nakahara

Department of Physics &

Research Centre for Quantum Computing

Kinki University, Japan

Plan of lecture

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

I. Introduction

Overview @ Tehran 2009

More complicated Example

Overview @ Tehran 2009

Quantum Computing/Information Processing

- Quantum computation & information processing make use of quantum systems to store and process information.
- Exponentially fast computation, totally safe cryptosystem, teleporting a quantum state are possible by making use of states & operations which do not exist in the classical world.

Overview @ Tehran 2009

Plan of lectures

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

2. Qubits

Overview @ Tehran 2009

2.1 One Qubit

Overview @ Tehran 2009

Candidates of qubits：

Electron,

Spin 1/2 Nucleus

Grand State and Excited State of Atom or Ion

Photon

Overview @ Tehran 2009

2.2 Two-Qubit System

Overview @ Tehran 2009

2.3 Multi-qubit systems and entangled states

Overview @ Tehran 2009

2.4 Algorithm = Unitary Matrix

Overview @ Tehran 2009

Physical Implementation of U

Overview @ Tehran 2009

Plan of lectures

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

3. Quantum Gates, Quantum Circuit and Quantum Computer

Overview @ Tehran 2009

3.2 Quantum Gates

Overview @ Tehran 2009

Hadamard transform

Overview @ Tehran 2009

n-qubit Operations

Overview @ Tehran 2009

Quantum Mechanics

Overview @ Tehran 2009

3.3 Universal Quantum Gates

Overview @ Tehran 2009

3.4 Quantum Parallelism and Entanglement

Overview @ Tehran 2009

Power of Entanglement

Overview @ Tehran 2009

Plan of lectures

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

4. Simple Quantum Algorithms4.1 Deutsch’s Algorithm

Overview @ Tehran 2009

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

Necessary Conditions for a PC to Work Properly

- Hardware (Memory, CPU etc),
- Able to reset all the memories to 0,
- The PC lasts till a computation stops (maybe a problem if it takes more than 10 years to finish the computation.)
- Able to carry out any logic operations
- Able to output the results (display, printer, …)

Overview @ Tehran 2009

Necessary Conditions for a Quantum Computer to Work Properly (DiVincenzo Criteria)

- A scalable physical system with well characterized qubits.
- The ability to initialize the state of the qubits to a simple fiducial state, such as |00…0>.
- Long decoherence times, much longer than the gate operation time.
- A “universal” set of quantum gates.
- A qubit-specific measurement capability.

- Hardware (Memory, CPU etc)
- Able to reset all the memories to 0,
- The PC lasts till a computation stops.
- Able to carry out any logic operations
- Able to output the results (display, printer, )

Overview @ Tehran 2009

DiVincenzo [email protected] Univ.

Overview @ Tehran 2009

Physical Realization: NMR

Overview @ Tehran 2009

Physical Realization: Trapped Ions

Overview @ Tehran 2009

Physical Realization: Josephson Junction Qubits

Overview @ Tehran 2009

Tunable coupling (interaction on demand)

Overview @ Tehran 2009

Physical Realization: Neutral Atoms

Overview @ Tehran 2009

Physical Realization: Quantum Dots

Overview @ Tehran 2009

- 1. Introduction
- 2. Qubits
- 3. Quantum Gates, Quantum Circuits and

Quantum Computer

- 4. Simple Quantum Algorithms
- 5. DiVincenzo Criteria & Physical Realizations
- 6. Shor’s Factorization Algorithm

Overview @ Tehran 2009

Difficulty of Prime Number Facotrization

- Factorization of N=89020836818747907956831989272091600303613264603794247032637647625631554961638351 is difficult.
- It is easy, in principle, to show the product of p=9281013205404131518475902447276973338969 and q =9591715349237194999547 050068718930514279 is N.
- This fact is used in RSA (Rivest-Shamir-Adleman) cryptosystem.

Overview @ Tehran 2009

Factorization algorithm

Overview @ Tehran 2009

Realization using NMR (15=3×5)L. M. K. Vandersypen et al (Nature 2001)

Overview @ Tehran 2009

NMR molecule and pulse sequence (~300 pulses)

perfluorobutadienyl iron complex with the two 13C-labelled

inner carbons

Overview @ Tehran 2009

Foolproof realization is discouraging …? Vartiainen, Niskanen, Nakahara, Salomaa (2004)

Foolproof implementation of the factorization 21=3 X 7 using Shor’s algorithm requires at least 22 qubits and approx. 82,000 steps!

Overview @ Tehran 2009

Summary

- Quantum information and computation are interesting field to study. (Job opportunities at industry/academia/military).
- It is a new branch of science and technology covering physics, mathematics, information science, chemistry and more.
- Thank you very much for your attention!

Overview @ Tehran 2009

Download Presentation

Connecting to Server..