Limitations CMOS scaling short channel effect hot carrier

Limitations • CMOS의 scaling 한계 – short channel effect (hot carrier effect) – thin oxide tunneling, etc. • Interconnection 문제 – speed limitation – thermal problem – cost • Critical length: 20~30 nm 4 서울시립대학교 양자정보처리연구단

What is quantum information processing? • A research in quantum information processing is to understand how quantum mechanics can improve acquisition, transmission and processing of information. Who may be involved? • • • Computer scientists Mathematicians Electrical engineers Chemists Physicists 8 서울시립대학교 양자정보처리연구단

• US research budget from $1 m in 1995 to $30 m in 2000 • Japanese spends about $10 m in 2001 • Three networks in EU • Australians have set up a q. comp. centre. 10 서울시립대학교 양자정보처리연구단

고전적인 정보처리 과정 Source Channel Destination • Source : Alphabet X와 각각의 빈도확률 Px로정의된 ensemble • Example : “ 0” 과 “ 1”로 정의된 Alphabet 집합 및 확률 P 0 와 P 1 – Channel Turing machine 통신 channel etc 11 서울시립대학교 양자정보처리연구단

N - qubit system • N-qubit system : H 2의 tensor product space H 2 = H 2 ··· H 2 n 2 n states ! N = 2 n : Probability exponential amount of computation space!!! 13 서울시립대학교 양자정보처리연구단

Gate • Classical gate : A • Quantum gate : UA : Unitary transformation 14 서울시립대학교 양자정보처리연구단

Deutch Problem : quantum parallelism (1) Black x box f(x) : constant : balanced Set 15 서울시립대학교 양자정보처리연구단

Deutch Problem : quantum parallelism (2) Set Output f(0)&f(1) can be calculated at the same time!!! 16 서울시립대학교 양자정보처리연구단

Deutch Problem : quantum parallelism (3) on N qubits Set Massive parallelism !!! (2 N outputs in one query) 17 서울시립대학교 양자정보처리연구단

RSA (Ronald Rivest, Adi Shamir, Leonard Adleman) encryption 1978 #1 i) prime number n = pq ii) find d GCD [ d, (p-1) (q-1) ] =1 iii) find e ed = 1 mod (p-1)(q-1) public key {e, n}, private key {d, n} v) Ei = mod n ; Mi = mod n 18 서울시립대학교 양자정보처리연구단

RSA #2 • Code-breaking need to find { d, n} i) find p, q n = pq ii) find e ed = 1 mod (p-1) (q-1) iii) Mi = mod n 19 서울시립대학교 양자정보처리연구단

RSA #3 factoring time Size of n (bits) => N = 2000 (bit) T > age of the universe 20 서울시립대학교 양자정보처리연구단

RSA #4 Let fn (a) = x a mod n such that GCD (x, n) =1 Then fn (a) becomes periodic function with period r Example n =5, x =3 x 0 mod n =1 x 1 mod n =3 x 2 mod n =4 x 3 mod n =2 x 4 mod n =1 => r = 4 21 서울시립대학교 양자정보처리연구단

RSA #5 then xr =1 mod n (x r/2)2 – 1 = 0 mod n (x r/2 – 1)( x r/2 + 1) = 0 mod n from GCD (x r/2 – 1, n) & GCD (x r/2 +1, n) => p, q Factoring problem of n is transformed to the problem of finding he period r of a function f n (a) = x a mod n !!! 22 서울시립대학교 양자정보처리연구단

Shor’s Algorithm 1) register 1: | > = 2) register 2: U| > = 3) Measurement : | > => 23 서울시립대학교 양자정보처리연구단

Only one article on quantum information processing? Of course, not. Quantum cryptography The end of the code war? - The use of quantum mechanics to encrypt messages may foil eavesdroppers and code-breakers for good. Jun 21 st 2001 The Economist 24 서울시립대학교 양자정보처리연구단

Controlled-Not gate ( Superposition entanglement ) : ( Swapping ) 25 서울시립대학교 양자정보처리연구단

Implementation : Two-spin systems #1 26 서울시립대학교 양자정보처리연구단

Implementation : Two-spin systems #2 27 서울시립대학교 양자정보처리연구단

Implementation : Two-spin systems #3 : spin flips !!! 28 서울시립대학교 양자정보처리연구단

Experimental environment for solid state qubit #1 Small dimension for larger quantum coupling Even such small system phase decoherence time < several hundred psec at m. K temperature Nano device technology Electrical time dependent measurement with 100 psec resolution at m. K temperature 30 서울시립대학교 양자정보처리연구단

Experimental environment for solid state qubit #2 Si nano transistor Room Temperature pulse generation sampling technique ( t~100 psec, 40 GHz BW Microwaveguide nano device m. K environment 서울시립대학교 양자정보처리연구단 stacked self assembled QD Single molecule by dip pen 31

Detailed aims and achievement of experiments Year Goal 1998 QD diode Achievement Si SAQD diode Transport in In. As SAQD ensemble In. As SAQD QD diode Signal detector incorporating many QDs (Floating dot memory) 1999 QD transistor Single QD signal detector Manipulation of QD array 2000 Coupled QD transistor Electronic transport in time domain Coupled QD signal detector Coupled Si QD transistor (development under progress) Stacked In. As SAQD diode Time-domain characterization of In. As SAQD diode (coherent control of superposed quantum states) Coupled Si QD signal detector (development under progress) Macro-modeling of SET circuits 서울시립대학교 양자정보처리연구단 32

What are grand challenges in quantum information processing? ØTo manufacture, manipulate and characterise arbitrary entangled systems. ØTo develop the fundamental theory of quantum entanglement. ØTo control decoherence and prove the scalability of quantum information processing. ØTo develop applications of the few qubit quantum information processor. ØTo master quantum coherences and understand the quantum-classical boundary. 33 서울시립대학교 양자정보처리연구단