quantum computing: an overview for non-specialists mikio nakahara department of physics &...
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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
Overview @ Tehran 2009
I. IntroductionI. 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
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2.1 One Qubit
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Candidates of qubits:
Electron,
Spin 1/2 Nucleus
Photon Grand State and Excited State of
Atom or Ion
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2.2 Two-Qubit System
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2.3 Multi-qubit systems and entangled states
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2.4 Algorithm = Unitary Matrix
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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,3. Quantum Gates, Quantum Circuit Quantum Circuit and Quantum Computerand Quantum Computer
Overview @ Tehran 2009
Overview @ Tehran 2009
3.2 Quantum Gates
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Hadamard transform
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Overview @ Tehran 2009
n-qubit Operations
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Quantum Mechanics
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3.3 Universal Quantum Gates
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3.4 Quantum Parallelism and Entanglement
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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. Simple Quantum Algorithms4.1 Deutsch’s Algorithm4.1 Deutsch’s Algorithm
Overview @ Tehran 2009
Overview @ Tehran 2009
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
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,
…)
Overview @ Tehran 2009
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.
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DiVincenzo 2004@Kinki Univ.
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Physical Realization: NMR
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Physical Realization: Trapped Ions
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Physical Realization: Josephson Junction Qubits
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Tunable coupling (interaction on demand)
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Physical Realization: Neutral Atoms
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Physical Realization: Quantum Dots
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
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.
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Factorization algorithm
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Realization using NMR (15=3×5)L. M. K. Vandersypen et al (Nature 2001)
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NMR molecule and pulse sequence (~300 pulses)
perfluorobutadienyl iron complex with the two 13C-labelledinner carbons
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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