1. Quantum Computer Implementations
Christopher Monroe
University of Michigan
Department of Physics
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. Moore’s Law
# Transistors
109
108
Pentium III
107
Pentium Pro
106
Pentium
i486
i386
1. The “real” Moore’s law is coming to a close. Molecular transistors, beyond that?
105
80286
104
8086
103
1975
1980
1985
1990
1995
2000
2005
2010
2015
Projected
Source: Intel

5. “There's Plenty of Room at the Bottom”
(1959 APS annual meeting)
Richard Feynman
“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…”

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

7. N qubits can store 2N numbers simultaneously
GOOD NEWS…
N qubits can store 2N 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
…BAD NEWS…
Measurement gives random result
e.g.,   |011
Good-bad-good. Exponential storage. X2 example of parallelism.

8. quantum interference before measurement
…GOOD NEWS!
quantum interference before measurement
quantum gates
depends on all inputs
|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
Shor started it all
Deutsch (1985)
Shor (1994)
Grover (1996)
fast number factoring

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

11. Quantum computer hardware requirements
Must make states like
|000…0 + |111…1 x +
strong coupling between qubits
weak coupling to environment
2. Must measure state with high efficiency
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. Trick: apply sinusoidal electric field (rotate saddle)
Ion Trap Primer +
E(r)
NO! E = 0
saddle point z
E(r) ? +
Trick: apply sinusoidal electric field (rotate saddle)
RF (PAUL) TRAP

15. Dynamics of a single ion in a rf trap
e = ion charge
m = ion mass
V0 = rf voltage amplitude
d = trapsize
x + [k2 cosWt]x = 0
k2 = eV0/md2
time
position x
“secular” motion
at frequency wtrap  k2/W  MHz
“micromotion”
at frequency W  100 MHz
Mathieu Equation: x(t) bounded for k << W

16. 3D ion trap geometry
endcap d V
ring
endcap

17. Michigan
Ion Trap
2 mm

18. 0.2 mm
|0
|1

19. “Perfect” quantum measurement of a single atom
state |0
state |1
# photons collected in 200ms
Probability 30 20 10
0.2
ion fluoresces 108 photons/sec
laser
laser
ion remains dark 30 20 10 1
# photons collected in 200ms
>99% detection efficiency!

20. Atomic Cd+ energy levels
or Be+, Mg+, Sr+, Ca+, Ba+, Cd+, Hg+,….
P3/2
215nm
~108
photons/sec
S1/2
|1
15GHz
|0

21. Coherent transitions between |0 and |1
P3/2
2-photon
“stimulated Raman”
transitions
S1/2
|1
|0
Coherent transitions between |0 and |1

22. Mapping: (|0 + |1) |0m  |0 (|0m + |1m) S1/2 |1
2-photon
“stimulated Raman”
transitions
Mapping: (|0 + |1) |0m  |0 (|0m + |1m) • 2 1 •
S1/2
|1 2 1
|0

23. Pulse Raman beams for time t Pulse Detection beams for 200 ms step t
Prepare in |0|rest 
Pulse Raman beams for time t
Pulse Detection beams for 200 ms
step t
Single ion transitions between
|0|rest  and |1 |moving  20 40 60 80
100 1
t (ms)
Prob(|0)
CM, et. al., Phys. Rev. Lett. 75, 4714 (1995)

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

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

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

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

30. “accumulator”

31. target quantum
bits entangled
laser
pulse

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

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)
m = -aE
U = -m•E = -a|E|2
U(x) = -a|E(x)|2
a = polarizability
lasers induce electric dipole
that interacts with laser itself!
l/2

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

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

40. cavity-QED: deterministically creating and storing
single photons in a resonator
qubit: |0 = zero photons in cavity
|1 = one photon in cavity L
Interaction strength
between atom & photon
U = -matom•E1  (Vol)1/2
L = 1 mm, t > 10-3sec
requires
Reflectivity > % M1 M2
atom

41. Quantum Network Cirac, Zoller, Kimble, Mabuchi, Phys. Rev. Lett
W(t)
W(-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)

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)
Optical Field
AlGaAs
GaAs
AlGaAs

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

53. Optical Field
AlGaAs
GaAs
AlGaAs
GaAs
AlGaAs

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

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. Electrons floating on liquid helium
Platzman and Dykman, Science 284 (1999)
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
works
scales

66. Quantum Computing Abyss
state-of-the-art
experiments
theoretical requirements
for “useful” QC
 5
# quantum bits
>1000
# quantum bits
<100
# logic gates
>109
noise
reduction
error
correction ?
new
technology
efficient
algorithms