Quantum Computing: An Overview for non-specialists Mikio Nakahara Department of Physics & Research...

Quantum Computing:Quantum Computing:An OverviewAn Overview

for non-specialistsfor non-specialists

Mikio NakaharaMikio NakaharaDepartment of Physics & Department of Physics & Research Centre for Quantum Research Centre for Quantum ComputingComputingKinki University, JapanKinki University, Japan

Financial supports from Kinki Univ.,

MEXT and JSPS

Overview @ Tehran 2009

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


I. IntroductionI. Introduction


More complicated Example


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.


Plan of lectures



2. Qubits


2.1 One Qubit


Candidates of qubits：

Electron,

Spin 1/2 Nucleus

Photon Grand State and Excited State of

Atom or Ion


2.2 Two-Qubit System


2.3 Multi-qubit systems and entangled states


2.4 Algorithm = Unitary Matrix


Physical Implementation of U


Plan of lectures



3. Quantum Gates,3. Quantum Gates, Quantum Circuit Quantum Circuit and Quantum Computerand Quantum Computer


3.2 Quantum Gates


Hadamard transform


n-qubit Operations


Quantum Mechanics


3.3 Universal Quantum Gates


3.4 Quantum Parallelism and Entanglement


Power of Entanglement


Plan of lectures



4. Simple Quantum Algorithms4. Simple Quantum Algorithms4.1 Deutsch’s Algorithm4.1 Deutsch’s Algorithm


Plan of lectures



Necessary Conditions for a PC to Work ProperlyNecessary 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,

…)


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

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, )

A scalable physical system with well charactA scalable physical system with well characterized qubits.erized qubits.

The ability to initialize the state of the qubits The ability to initialize the state of the qubits to a simple fiducial state, such as |00…0>.to a simple fiducial state, such as |00…0>.

Long decoherence times, much longer than Long decoherence times, much longer than the gate operation time.the gate operation time.

A “universal” set of quantum gates.A “universal” set of quantum gates. A qubit-specific measurement capability.A qubit-specific measurement capability.


DiVincenzo 2004@Kinki Univ.


Physical Realization: NMR


Physical Realization: Trapped Ions


Physical Realization: Josephson Junction Qubits


Tunable coupling (interaction on demand)


Physical Realization: Neutral Atoms


Physical Realization: Quantum Dots


Plan of lectures



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.


Factorization algorithm


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


NMR molecule and pulse sequence (~300 pulses)

perfluorobutadienyl iron complex with the two 13C-labelledinner carbons


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!


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!

Quantum Computing: An Overview for non-specialists Mikio Nakahara Department of Physics & Research...

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