quantum computer implementations university of michigan department of physics christopher monroe us...
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Quantum Computer Implementations
University of MichiganDepartment of Physics
http://monroelab2.physics.lsa.umich.edu/
Christopher Monroe
US Advanced Research andDevelopment Activity
US Army Research Office
US National Security Agency National Science Foundation
ENIAC(1946)
The first solid-state transistor
(Bardeen, Brattain & Shockley, 1947)
19751980
19851990
19952000
20052010
2015
808680286
i386i486
PentiumPentium Pro
Source: Intel
Projected
103
104
105
106
107
108
109
# Transistors
Moore’s LawMoore’s Law
Pentium III
“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
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
…BAD NEWS…Measurement gives random result
e.g., |011
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
…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 quantumXOR gate:
superposition entanglement
depends on all inputs
quantum
gates
fast number factoring
Quantum Entanglement: Einstein’s “Spooky action-at-a-distance”
or or
“superposition” “entangled superposition”
Quantum computer hardware requirements
1. Must make states like
|000…0 + |111…1 xx+
2. Must measure state with high efficiency
• strong coupling between qubits• weak coupling to environment
•strong coupling to environment
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
0.3 mm
Ion Trap Primer
+
E(r) ?
+
E(r)
NO! E saddle point
z
Trick: apply sinusoidal electric field (rotate saddle)
RF (PAUL) TRAP
x + [2 cost]x = 0
2 = eV0/md2
Dynamics of a single ion in a rf trap
e = ion charge m =ion mass V0 =rf voltage amplitude d =trapsize
timepos
itio
n x
“secular” motionat frequency trap 2/ MHz
“micromotion”at frequency 100 MHz
Mathieu Equation: x(t) bounded for <<
V
3D ion trap geometry
ring
endcap
endcap
d
2 m
MichiganIon Trap
0.2 mm
|0
|1
““Perfect” quantum measurement of a single atomPerfect” quantum measurement of a single atom
state |0 state |1
# photons collected in 200s
Pro
babili
ty
30201000
0.2
ion fluoresces 108 photons/sec
laser laser
ion remains dark
30201000
1
# photons collected in 200s
>99% detection efficiency!
Atomic Cd+ energy levels or Be+, Mg+, Sr+, Ca+, Ba+, Cd+, Hg+,….
S1/2
P3/2
|1
|0
~108
photons/sec
215nm
15GHz
S1/2
P3/2
|1
|0
2-photon“stimulated
Raman”transitions
Coherent transitions between |0 and |1
•••
01
2
•••
01
2S1/2
P3/2
|1
|0
2-photon“stimulated
Raman”transitions
Mapping: (|0 + |1) |0m |0 (|0m + |1m)
0 20 40 60 80 100
0
1
(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)
Trapped Ion Quantum ComputerTrapped 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. Cirac and Zoller, Phys. Rev. Lett. 7474, 4091 (1995), 4091 (1995)
State-of-the-art:Four-qubit
quantum logic gate
Sackett, et al., Nature 404, 256 (2000)
|0000 |0000 + ei|1111
Why only 4 ?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
quantummemory
“refrigerator” ions suppress motional
decoherence
Scaling proposal 1: the “quantum CCD”
few mm
(Kielpinski, Monroe, Wineland, submitted to Nature)
“accumulator”
target quantum
bits entangled
laserpulse
motion
head
targetpushinglaser
Scaling proposal 2: ion trap array and head
Cirac and Zoller, Nature 404, 579-581 (2000).
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Optical Lattices (trapped neutral atoms)
/2
lasers induce electric dipolethat interacts with laser itself!
= E
U = •E = |E|2
U(x) = |E(x)|2
polarizability
moving neutral atoms qubits together for entanglement
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Individual photons
A
B
|1 = |0A|1B + |1A|0BQuantum
Entanglement!send singlephotons
50/50
weaklaser
qubit: |0 = zero photons|1 = one photon
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,…)
M1 M2
Interaction strength between atom & photon U = atom•E1 (Vol)1/2
L = 1 mm, > 10-3secrequiresReflectivity > 99.999999%
atom
L
qubit: |0 = zero photons in cavity|1 = one photon in cavity
cavity-QED: deterministically creating and storing single photons in a resonator
Quantum Network Cirac, Zoller, Kimble, Mabuchi, Phys. Rev. Lett. 78, 3221 (1997)
(t)
(-t)
H.J. Kimble(CalTech)
M. Chapman(Georgia Tech)
G. Rempe(Max Planck Inst.,Garching)
H. J. Kimble, CalTech
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Superconducting charges Nakamura (NEC-Japan)Schoelkopf (Yale)Devoret (Yale)
Single-qubit rotations on a Cooper-pair Box
|N |N+1 (N=# Cooper pairs)
Nakamura, et. al., Nature 398, 786 (1999)
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Superconducting currents J.E. Mooij,… Science 285, 1036 (1999).
quantized flux qubit states
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Semiconductor Quantum Dotse.g., Duncan Steel (University of Michigan)
GaAs
AlGaAs
AlGaAs
Optical Field
~10.5 ps
~18.5 ps
Exc
iton
Pop
ula
tion
Pulse Area
Excitonic Rabi oscillations
T. Stievater, et al. (submitted)
GaAs
AlGaAs
AlGaAs
Optical Field
GaAs
AlGaAs
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
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)
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
Platzman and Dykman, Science 284 (1999)
Electrons floating on liquid helium
1-dimensional “atom”
geometry
readout
positive bias appliedimaging channel plate
… electrons tunnel outonly if in state 2
Fabrication of submerged electrodes(J. Goodkind, UCSD)
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
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 inphosphorusnuclear spin
(P: spin-1/2)(Si: spin 0)
Single-qubit rotations:
electron/nuclearspin-spin interaction(hyperfine interaction)
Two-qubit entangling gates:
bring adjacent donorelectrons together (exchange interaction)
Physical Implementations
1. Individual atoms and photonsa. ion trapsb. atoms in optical latticesc. photon downconversion and cavity-QED
2. Superconductorsa. Cooper-pair boxes (charge qubits)b. rf-SQUIDS (flux qubits)
3. Semiconductorsquantum dots
4. Other condensed-mattera. NMRb. electrons floating on liquid heliumc. single phosphorus atoms in silicon
scales
works
Quantum Computing Abyss
?noise
reduction
newtechnology
# quantum bits
errorcorrection
efficientalgorithms
5 >1000
<100 >109
theoretical requirementsfor “useful” QC
state-of-the-artexperiments
# quantum bits
# logic gates