2. Basic Principles of Quantum computing I Soonchil Lee Dept. of physics, KAIST

3. 1 MIPS 컴퓨터로 10 16 개의 자료 중 하나를 찾을 때 – 고전컴퓨터 : 300 년 – 양자컴퓨터 : 1 분 현대 암호는 모두 NSA 에서 개발 양자전산 개발을 늦추면 암호종속 모든 정보의 일방적 유출 양자전산의 중요성

4. Quantum computing OUTPUT U INPUT Classical computing INPUT OUTPUT GATE

5. Ex) NOT operation H

6. 고전전산양자전산 비트상태 전압 0V & 5V 상태 중첩가능 양자고유상태 - 중첩가능 Ex)spin up & down Photon olarization 연산자 반도체게이트 Unitary operation 진화연산자 Optical device 알고리듬 수행 게이트의 공간 적 배열을 비 트가 통과 고정된 비트에 연산이 시간 적으로 수행됨

7. Classical computing INPUTOUTPUT GATEEx) ADDER

8. Quantum computing INPUTOUTPUT GATE Ex) U1U1 U2U2 U3U3 t U1U1 U2U2 U3U3

9. Execution of quantum algorithm (1) Algorithm development = a unitary operator U (2) Decomposition of U : U=U 1 U 2 U 3 … (programming) where and H i is a part of (3) Real pulse sequence design ( compile ) Any unitary operator can be expressed as a sequence of single qubit operators and controlled-NOT operators.

10. Single qubit operation H M |1> |0>

11. * Single qubit operation Single qubit operation is done by an rf pulse.

12. * Controlled-NOT operation Controlled-NOT gate where and Controlled-NOT is done by just waiting.

13. Controlled-NOT |10> |11> |01> |00> U CTCT CTCT

14. 54321 3 f(x)=0 Classical computing |1>+|2>+|3>+…. f(x)=0 |3> Quantum computing

15. Quantum parallel processing Classical parallel processing cannot imitate because 1.N qubit represents 2 N states. 2.entanglement |1>+|2> = |0> A |1> B +|1> A |0> B

16. Shor ’ s factorization algorithm –QC : (logN) 2+x steps (x<<1) –classical computer : exp{N 1/3 (logN) 2/3 } – 공개열쇠암호체계 격파 Grover ’ s search algorithm –for N data search, QC : N 1/2 try classical computer : N/2 try ex) if N=2 56 & 1 MIPS, 1000 year vs. 4 min. – 비밀열쇠암호체계 격파

17. 핵자기공명 (NMR: Nuclear Magnetic Resonance) - 대표적인 핵스핀 조작기법 1) J. Kim, J.-S. Lee, and S. Lee, Phys. Rev. A 61, 032312 (2000). 2) J. Kim, J.-S. Lee, S. Lee, and C. Cheong, submitted to Phys. Rev. A

18. Requirements for a Quantum Computer (1) qubit : two quantum states with good quantum # (2) Set : by measurement or thermal equilibrium ex) (3) Read (4) Single qubit operation (addressible): physical addressing or resonance tech. (5) Interaction (controllable) : well defined and on-off ------------------------------------------------------------- (6) Coherence : isolation from environment (and other qubits) (7) Scalability

19. (1) qubit - two states with good quantum # energy : el. floating in LHe charge : quantum dot spin : quantum dot, molecular magnet, ion trap, NMR, Si-based QC photon : optical QC, cavity QED cooper pair : superconductor fluxoid : superconductor

20. Requirements for a Quantum Computer (1) qubit :SPIN (2) Set : by measurement or thermal equilibrium ex) (3) Read (4) Single qubit operation (addressible): physical addressing or resonance tech. (5) Interaction (controllable) : well defined and on-off (6) Coherence : isolation from environment (and other qubits)

21. (6) Long coherence : Isolate qubits in vacuum : ion trap, el. floating in LHe by flying : methods using photon, el’s trapped by SAW or magnetic field in molecule : NMR in quantum well : quantum dot, superconductor inside solid : Si-based QC

22. Requirements for a Quantum Computer (1) qubit :SPIN (2) Set : by measurement or thermal equilibrium ex) (3) Read (4) Single qubit operation (addressible): (5) Interaction (controllable) : well defined and on-off (6) Coherence : solid state device

23. Magnetic Resonance Force Microscopy (MRFM) - Scanning Probe 와 공명의 결합 - 단일스핀 감지

24. Requirements for a Quantum Computer (1) qubit :SPIN (2) Set (3) Read : Single spin detection (4) Single qubit operation (addressible): (5) Interaction control (6) Coherence : solid state device

25. Ion trap Qubit - ion spin state Single spin operation - laser Inertaction - vibration(CM motion)

26. Environment measurement EM field

27. Basic Principles of Quantum computing II Soonchil Lee Dept. of physics, KAIST

28. 10 years ago… 1 st demonstration of quantum computing by NMR

29. For 5 years after then… We were excited by new challenge. Had a hard time to understand new concepts. Lots of NMR QC papers were published. Realized keys of a practical QC. Pedestrians show interests. Found that NMR is NOT a future QC. NMR QC experiment is needed no more.

30. Things change. Now … Developing a Practical Quantum Computer is the key issue. TheoryExperiment

31. Electron beam el. floating on liquid He el. trapped by SAW el. trapped by magnetic field Atomic and Molecular Ion trap Cavity QED NMR Molecular magnet N@C 60 (fullerine) BEC Solid State Quantum dot Superconductor Si-based QCOptical Photon Photonic crystal Quantum systems suggested as QC

32. Requirements for a Quantum Computer (1)Qubit : two quantum states with good quantum # (2) Read : Detection (3) Single qubit operation (addressible) (4) Interaction (controllable) : well defined and on-off (5) Coherence : isolation from environment (6) Scalability

33. Photon Quantum dot Josephson NMR Ion trap Si-base QC Qubit 0 …. 5 …. 10 … 20 …..100 2007.11 Practical Quantum computer

34. Si-based QC (Kane model) Si P electrode insulator rf coil magnet

35. Si-based QC (Kane model) Si P Qubit : nuclear spin of P Coherence time at 1.5 K el. spin ~ 10 3 S n. spin ~ 10 h Silicon technology Qubit Read Addressing Interaction Coherence Scalability

36. Qubit Read Addressing Interaction Coherence Scalability Si-based QC (Kane model) H rf coil magnet ? ?

37. rf coil magnet Single qubit operation (addressing) - hyperfine interaction engineering H H total = H ext +H hyp Use electric field to change H hyp

38. Single qubit operation (addressing) -hyperfine interaction engineering rf coil P atom B. Kane, Nature 393, 133 (1998) ++

39. Interaction control - RKKY interaction engineering 10nm electrode

40. arXiv:cond-mat/0104569 Australian Work

41. Kane Model P doped Silicon Single spin detection (SET, MRFM) Ensemble detection (NMR) Our strategy

42. Verification of Kane’s QC model 1 st step –Detection of P NMR signal 2 nd step –Hyperfine interaction control by E field 3 rd step –RKKY interaction control by E field

43. 1 st step of Verification of Kane’s QC Detection of P NMR signal - never done –Fix fluctuating electron spin by low T and high H to sharpen spectrum. rf coil H H total = H ext +H hyp

44. Low H High T High H Low T

45. Experiment P NMR of Si:P with n ~ 1x10 17 /cm 3 Temp : 45 mK ~ 3.5 K Field : 7.3 Tesla 3 He/ 4 He Dilution Refrigerator (Low Temperature Physics Lab. Kyoto Univ. )

46. No signal yet

47. H ex HeHe

48. HeHe E field

49. H ex HeHe HnHn

50. NMR - Direct Approach Electrical control of NMR frequency H hyp

51. Alternative Approach - ESR H hf

52. Quantum Information Science Developing a practical quantum computer is the key issue. We are on a normal research track after the initial excitement. Development goes with nanotechnology. Eventually we will get it!

53. The END The END

54. frequency shiftDetection of frequency shift by E field –hyperfine interaction control rf coil 2nd step of Verification of Kane’s QC H

55. Spectral shape changeSpectral shape change by electric field –RKKY interaction control rf coil 3rd step of Verification of Kane’s QC

56. ENDOR - Sample concentration < 1×10 16 /cm 3 - Temperature < 4K - Magnetic field T~3.3KG and frequency~9GHz We can check NMR frequency shift by ENDOR