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

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).






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






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






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)






Superconducting currents J.E. Mooij,… Science 285, 1036 (1999).

quantized flux qubit states






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






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)






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)






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)






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

Documents

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