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Basic Principles of Quantum computing I

Basic Principles of Quantum computing I. Soonchil Lee Dept. of physics, KAIST. 양자전산의 중요성. 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. Classical computing. Quantum computing. INPUT. OUTPUT. GATE.

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Basic Principles of Quantum computing I

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

  2. 양자전산의 중요성 • 1 MIPS 컴퓨터로 1016개의 자료 중 하나를 찾을 때 • 고전컴퓨터 : 300 년 • 양자컴퓨터 : 1 분 • 현대 암호는 모두 NSA에서 개발 • 양자전산 개발을 늦추면 암호종속 • 모든 정보의 일방적 유출

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

  4. Ex) NOT operation H

  5. Ex) ADDER Classical computing GATE INPUT OUTPUT

  6. Ex) U1 U1 U2 U3 U2 U3 t Quantum computing GATE INPUT OUTPUT

  7. Execution of quantum algorithm (1) Algorithm development = a unitary operator U (2) Decomposition of U : U=U1U2U3…(programming) where and Hi 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.

  8. |1> M |0> H Single qubit operation

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

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

  11. C T C T U |11> |01> |10> |00> Controlled-NOT

  12. Classical computing f(x)=0 3 3 5 4 2 1 Quantum computing f(x)=0 |1>+|2>+|3>+…. |3>

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

  14. Shor’s factorization algorithm • QC : (logN)2+x steps (x<<1) • classical computer : exp{N1/3(logN)2/3} • 공개열쇠암호체계 격파 • Grover’s search algorithm • for N data search, QC : N1/2 try • classical computer : N/2 try • ex) if N=256 & 1 MIPS, 1000 year vs. 4 min. • 비밀열쇠암호체계 격파

  15. 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

  16. Requirements for a Quantum Computer (1)qubit: twoquantum 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

  17. (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

  18. 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)

  19. (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

  20. 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

  21. Magnetic Resonance Force Microscopy (MRFM) - Scanning Probe와 공명의 결합 - 단일스핀 감지

  22. 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

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

  24. Environment EM field measurement

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

  26. 10 years ago… • 1st demonstration of quantum computing by NMR

  27. 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.

  28. Experiment Theory Things change. Now… • Developing a Practical Quantum Computer is the key issue.

  29. Quantum systems suggested as QC Atomic and Molecular Ion trap Cavity QED NMR Molecular magnet N@C60(fullerine) BEC Solid State Quantum dot Superconductor Si-based QC Optical Photon Photonic crystal Electron beam el. floating on liquid He el. trapped by SAW el. trapped by magnetic field

  30. Requirements for a Quantum Computer • Qubit : • twoquantum 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

  31. 2007.11 Photon Quantum dot Josephson Practical Quantum computer Ion trap NMR Si-base QC …..100 0 …. 5 …. 10 … 20 Qubit

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

  33. Si-based QC (Kane model) Qubit Read Addressing Interaction Coherence Scalability Si P • Qubit : nuclear spin of P • Coherence time at 1.5 K • el. spin ~ 103 S • n. spin ~ 10h • Silicon technology

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

  35. H rf coil magnet Single qubit operation (addressing) -hyperfine interaction engineering Htotal = Hext+Hhyp Use electric field to change Hhyp

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

  37. Interaction control - RKKY interaction engineering electrode 10nm

  38. Australian Work arXiv:cond-mat/0104569

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

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

  41. 1st 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 Htotal = Hext+Hhyp

  42. Low H High T High H Low T

  43. Experiment • P NMR of Si:P with n ~ 1x1017 /cm3 Temp : 45 mK ~ 3.5 K Field : 7.3 Tesla 3He/4He Dilution Refrigerator (Low Temperature Physics Lab. Kyoto Univ. )

  44. No signal yet

  45. He Hex

  46. He Hex E field

  47. He Hn Hex Hex

  48. NMR - Direct Approach Hhyp Electrical control of NMR frequency

  49. Alternative Approach- ESR Hhf

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