quantum computing an overview for non specialists
Download
Skip this Video
Download Presentation
Quantum Computing: An Overview for non-specialists

Loading in 2 Seconds...

play fullscreen
1 / 47

Quantum Computing: An Overview for non-specialists - PowerPoint PPT Presentation


  • 52 Views
  • Uploaded on

Financial supports from Kinki Univ., MEXT and JSPS. Quantum Computing: An Overview for non-specialists. Mikio Nakahara Department of Physics & Research Centre for Quantum Computing Kinki University, Japan. Plan of lecture. 1. Introduction 2. Qubits

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
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
quantum computing an overview for non specialists
Financial supports from Kinki Univ.,

MEXT and JSPS

Quantum Computing:An Overviewfor non-specialists

Mikio Nakahara

Department of Physics &

Research Centre for Quantum Computing

Kinki University, Japan

plan of lecture
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
I. Introduction

Overview @ Tehran 2009

more complicated example
More complicated Example

Overview @ Tehran 2009

quantum computing information processing
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
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
2. Qubits

Overview @ Tehran 2009

2 1 one qubit
2.1 One Qubit

Overview @ Tehran 2009

candidates of qubits
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
2.2 Two-Qubit System

Overview @ Tehran 2009

2 4 algorithm unitary matrix
2.4 Algorithm = Unitary Matrix

Overview @ Tehran 2009

physical implementation of u
Physical Implementation of U

Overview @ Tehran 2009

plan of lectures14
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 2 quantum gates
3.2 Quantum Gates

Overview @ Tehran 2009

hadamard transform
Hadamard transform

Overview @ Tehran 2009

n qubit operations
n-qubit Operations

Overview @ Tehran 2009

quantum mechanics
Quantum Mechanics

Overview @ Tehran 2009

3 3 universal quantum gates
3.3 Universal Quantum Gates

Overview @ Tehran 2009

power of entanglement
Power of Entanglement

Overview @ Tehran 2009

plan of lectures25
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

plan of lectures29
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

necessary conditions for a pc to work properly
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
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

physical realization nmr
Physical Realization: NMR

Overview @ Tehran 2009

plan of lectures39
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

difficulty of prime number facotrization
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
Factorization algorithm

Overview @ Tehran 2009

nmr molecule and pulse sequence 300 pulses
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 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
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

ad