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Quantum Computer Implementations University of Michigan Department of Physics Christopher Monroe US Advanced Research.

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Presentation on theme: "Quantum Computer Implementations University of Michigan Department of Physics Christopher Monroe US Advanced Research."— Presentation transcript:

1 Quantum Computer Implementations University of Michigan Department of Physics Christopher Monroe US Advanced Research and Development Activity US Army Research Office US National Security Agency National Science Foundation

2 ENIAC (1946)

3 The first solid-state transistor (Bardeen, Brattain & Shockley, 1947)

4 i386 i486 Pentium Pentium Pro Source: Intel Projected # Transistors Moore’s Law Pentium III

5 “When we get to the very, very small world – say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics…” “There's Plenty of Room at the Bottom” (1959 APS annual meeting) Richard Feynman

6 A quantum computer hosts quantum bits which can store superpositions of 0 and 1 classical bit: 0 or 1 quantum bit:  |0  +  |1  Benioff (1980) Feynman (1982) “qubit” = two-level system |0  |1  |0  |1 

7 …BAD NEWS… Measurement gives random result e.g.,   |011  GOOD NEWS… N qubits can store 2 N numbers simultaneously Example: N=3 qubits  =a 0 |000  + a 1 |001  + a 2 |010  + a 3 |011  a 4 |100  + a 5 |101  + a 6 |110  + a 7 |111 

8 …GOOD NEWS! quantum interference before measurement Deutsch (1985) Shor (1994) Grover (1996) |0  |0   |0  |0  |0  |1   |0  |1  |1  |0   |1  |1  |1  |1   |1  |0  e.g., ( |0  + |1  ) |0   |0  |0  + |1  |1  quantum XOR gate: superposition  entanglement depends on all inputs quantu m gates fast number factoring

9 Quantum Entanglement: Einstein’s “Spooky action-at-a-distance” or “superposition” “entangled superposition”

10

11 Quantum computer hardware requirements 1.Must make states like |000…0  + |111…1  x x + 2. Must measure state with high efficiency strong coupling between qubits weak coupling to environment strong coupling to environment

12 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

13 0.3 mm

14 Ion Trap Primer + E(r) ? + E(r) NO!  E  saddle point z Trick: apply sinusoidal electric field (rotate saddle) RF (PAUL) TRAP

15 x + [  2 cos  t]x = 0  2 = eV 0 /md 2  Dynamics of a single ion in a rf trap e= ion charge m=ion mass V 0 =rf voltage amplitude d=trapsize time position x “secular” motion at frequency  trap   2 /   MHz “micromotion” at frequency  100 MHz Mathieu Equation: x(t) bounded for  << 

16 V 3D ion trap geometry ring endcap d

17 2  m Michigan Ion Trap

18 0.2 mm |0  |1 

19 “Perfect” quantum measurement of a single atom state |0  state |1  # photons collected in 200  s Probability ion fluoresces 10 8 photons/sec laser ion remains dark # photons collected in 200  s >99% detection efficiency!

20 Atomic Cd + energy levels or Be +, Mg +, Sr +, Ca +, Ba +, Cd +, Hg +,…. S 1/2 P 3/2 |1  |0  ~10 8 photons/sec  215nm  15GHz

21 S 1/2 P 3/2 |1  |0  2-photon “stimulated Raman” transitions Coherent transitions between |0  and |1 

22 S 1/2 P 3/2 |1  |0  2-photon “stimulated Raman” transitions Mapping: (  |0  +  |1  ) |0  m  |0  (  |0  m +  |1  m )

23  (  s) Prob(|0  ) Single ion transitions between |0  |rest  and |1  |moving  Prepare in |0  |rest  Pulse Raman beams for time  Pulse Detection beams for 200 ms step  CM, et. al., Phys. Rev. Lett. 75, 4714 (1995)

24 Trapped Ion Quantum Computer laser cool to rest laser j k map j th qubit to collective motion laser j k flip k th qubit if collective motion laser j k map collective motion back to j th qubit Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995) Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

25 State-of-the-art: Four-qubit quantum logic gate Sackett, et al., Nature 404, 256 (2000) |0000   |0000  + e i  |1111 

26

27

28 Why only 4 ? fluctuating electric patch potentials on surface technical, not fundamental limitation More ions: difficult (& slow) to isolate single mode of motion Decoherence of motion: 0.5 mm

29 quantum memory “refrigerator” ions suppress motional decoherence Scaling proposal 1: the “quantum CCD” few mm (Kielpinski, Monroe, Wineland, submitted to Nature)

30 “accumulator”

31 target quantum bits entangled laser pulse

32

33 motion head target pushing laser Scaling proposal 2: ion trap array and head Cirac and Zoller, Nature 404, (2000).

34 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

35 Optical Lattices (trapped neutral atoms) /2 lasers induce electric dipole that interacts with laser itself!  =  E U = E =  |E| 2 U(x) =  |E(x)| 2  polarizability

36 moving neutral atoms qubits together for entanglement

37 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

38 Individual photons A B |  1  = |0  A |1  B + |1  A |0  B Quantum Entanglement! send single photons 50/50 weak laser qubit: |0  = zero photons |1  = one photon

39 single photon source: optical parametric downconversion BUT… not scalable! Prob(downconversion)~10 -8 ultraviolet ( ) visible (or infrared) (  ) X  (2) nonlinear crystal (e.g., ADP, BBO,…)

40 M1 M2 Interaction strength between atom & photon U =  atomE 1  (Vol) 1/2 L = 1 mm,  > sec requires Reflectivity > % atom L qubit: |0  = zero photons in cavity |1  = one photon in cavity cavity-QED: deterministically creating and storing single photons in a resonator

41 Quantum Network Cirac, Zoller, Kimble, Mabuchi, Phys. Rev. Lett. 78, 3221 (1997)  (t)  (-t)

42 H.J. Kimble (CalTech) M. Chapman (Georgia Tech) G. Rempe (Max Planck Inst., Garching)

43 H. J. Kimble, CalTech

44 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

45 Superconducting charges Nakamura (NEC-Japan) Schoelkopf (Yale) Devoret (Yale)

46

47 Single-qubit rotations on a Cooper-pair Box |N   |N+1  (N=# Cooper pairs) Nakamura, et. al., Nature 398, 786 (1999)

48 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

49 Superconducting currents J.E. Mooij,… Science 285, 1036 (1999). quantized flux qubit states

50 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

51 Semiconductor Quantum Dots e.g., Duncan Steel (University of Michigan) GaAs AlGaAs Optical Field

52  ~10.5 ps  ~18.5 ps Exciton Population Pulse Area Excitonic Rabi oscillations T. Stievater, et al. (submitted)

53 GaAs AlGaAs Optical Field GaAs AlGaAs

54

55 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

56 Nuclear Magnetic Resonance liquid state, room temperature NMR several “qubit operations” demonstrated, BUT: no entanglement not scalable (signal decreases exponentially with # qubits) (not quantum computing?) Gershenfeld and Chuang, Science 275, 350 (1997)

57 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

58 Platzman and Dykman, Science 284 (1999) Electrons floating on liquid helium 1-dimensional “atom”

59 geometry

60 readout positive bias applied imaging channel plate … electrons tunnel out only if in state 2

61 Fabrication of submerged electrodes (J. Goodkind, UCSD)

62 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

63 Phosphorus atoms in Silicon Kane, Nature 393, 133 (1998) U. Maryland, Los Alamos, Australia NOTE: Bruce Kane will give Physics Dept. colloquium Wed., Nov. 7, 4PM qubit stored in phosphorus nuclear spin (P: spin-1/2) (Si: spin 0)

64 Single-qubit rotations: electron/nuclear spin-spin interaction (hyperfine interaction) Two-qubit entangling gates: bring adjacent donor electrons together (exchange interaction)

65 Physical Implementations 1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon scales works

66 Quantum Computing Abyss ? noise reduction new technology # quantum bits error correction efficient algorithms  5 5>1000 <100>10 9 theoretical requirements for “useful” QC state-of-the-art experiments # quantum bits # logic gates

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