Download
1 / 47
480 likes | 690 Views
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
E N D
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 • 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
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 • 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 2004@Kinki 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
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. 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
