Quantum Information Processing with Trapped Ions

1
Quantum Information Processing with Trapped Ions
NIST-Boulder Ion QC group
E. Knill C. Langer D. Leibfried R. Reichle S.
Seidelin T. Schaetz D. J. Wineland

• R. Ozeri
• M. Barrett
• J. Britton
• B. R. Blakestad
• J. Chiaverini
• W. M. Itano
• D. Hume
• J. D. Jost

Be
Be
2
Overview

• Trapped ions Experimental System
• The trap
• Initialization, detection.
• Coherent control of the ion-qubit
• Deterministic entanglement
• Deterministic Teleportation Between Atomic
  Qubits.
• Quantum Error-Correction.

3
Linear RF Paul trap
Positive ion
RF electrode
High dc potential control electrode
Low dc voltage control electrode

• Drive freq 100-150 MHz
• RF amp 200-400 V
• Secular freq
• Radial 15 MHz
• Axial 4 MHz

4
Multi-zone ion trap

• Gold on alumina construction
• RF quadrupole realized in two layers
• Six trapping zones
• Both loading and experimental zones
• One narrow separation zone
• Closest electrode 140 mm from ion

rf filter board
segmented linear trapping region
1 cm
control
rf
view along axis
rf
control
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Ion transport

• Ions can be moved between traps.
• Electrode potentials varied with time
• Ions can be separated efficiently in sep. zone
• Small electrodes potential raised
• Motion (relatively) fast
• Shuttling several 10 ms
• Separating few 100 ms

200 ?m
separation zone
100 ?m
6-zone alumina/gold trap(Murray Barrett, Tobias
Schaetz et al.)
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Electronic levels in 9Be
2P3/2
Fine structure
(P also has hfs, but its negligible)
2P
197 GHz
2P1/2
Hyperfine structure
Turn on small B field
F 1
2S1/2
1.25 GHz
F 2
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Qubit levels in 9Be
2P3/2
2P1/2
Vibrational mode quantum number
ñ1ñ ñ0ñ
F 1
mF 0
???
mF -1
mF 1
2S1/2
1.25 GHz
mF 2
F 2
mF 1
ñ1ñ ñ0ñ
mF 0
???
mF -1
mF -2
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Cooling and initialization
2P3/2
2P1/2
Raman side-band cooling Optical pumping Ion
initialized in the ñ0ñ, with better than 99
efficiency.
mF 0
???
mF -1
mF 1
2S1/2
1.25 GHz
mF 2
mF 1
mF 0
???
mF -1
mF -2
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Qubit detection by resonance fluorescence
2P3/2
2P1/2
Detection (s-)
 ??? ? ?F 2, mF -2?  ??? ? ?F 1, mF -1?
Detection efficiency gt99
313 nm
???
2S1/2
1.25 GHz
???
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Coherent control of qubits
2P3/2
80 GHz
2P1/2
k2
k1
Raman
Vib. mode quantum
313 nm
???
ñ1ñ ñ0ñ
2S1/2
1.25 GHz
???
ñ1ñ ñ0ñ
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Coherent qubit rotations
Bloch sphere
ñ
ñ - ñ
ñ i ñ
ñ - i ñ
ñ
ñ ñ
ñ
ñ

• Any single qubit rotation can be composed of 1-3
  pulses

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Entanglement on demand

• Geometric phase gate

Long. motional modes
1st mode (COM)
2nd mode (stretch)
Set ion spacing such that stretch is not excited
for ñ or ñ. Can give opposite spin states a
phase relative to same spin states.
Polarization gradient walking-standing wave
F -2F
Brennen, et al. PRL 1999 Jaksch, et al. PRL
1999 Mandel, et al. Nature 2003
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Phase gate
(Universal 2-qubit gate)
Tune d from stretch mode, displace for t2p/d
p
Start with ñ Perform p/2-D-3p/2 obtain, with
fidelity0.97
A
ñ or ñ
x
Df p/2
( ñ i ñ )/Ö2
p
ñ or ñ
x
Df 0
(Didi Leibfried et al. Nature 2003)
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Good year for the ions!

• Deterministic teleportation between atomic
  qubits. (NIST Innsbruck)
• Quantum error-correction with atomic qubits.
• Implementation of a semmi-classical Quantum
  Fourier transform.

• Creation of and spectroscopy with GHZ states.
  (NIST Innsbruck)
• Enhanced state detection efficiency with QIP .
• Quantum Dense coding

(M. Barrett et al. Nature 2004)
(D. Leibfried et al. Science 2004)
(M. Riebe et al. Nature 2004)
(C. F. Roos et al. Science 2004)
(J. Chiaverini et al. Nature 2004)
(T. Schaetz et al. PRL 2004)
(T. Schaetz et al. PRL 2004)
(J. Chiaverini et al. Submitted)
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Quantum teleportation
Bennet et al., 1993
Arbitrary state to be teleported
Bell state measurement
Distribute entanglement
Entangle pair
A
Apply conditional operation
B
Transmit classical information

• Resources required 2 cbits entangled pair

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Properties of Q. Teleportation

• Effectively transmit a qubit
• Use a classical channel
• Actually transmit only 2 cbits
• To classically define qubit infinite of cbits
• No information contained in 2 cbits
• Information in the correlations
• Entangled pair can be distributed anytime
• Initial qubit contains no info afterward

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QT in the lab
Alice prepares state to be teleported ( añ2
bñ2 )( ñ1ñ3 - ñ1ñ3 )
Create entangled state on outer ions ñ1ñ2ñ3
- ñ1ñ2ñ3
Alice performs Bell basis decoding using phase
gate on ions 1 and 2
Bob performs conditional rotation dep. on meas.
Bob recovers añ bñ on ion 3 and checks the
state
Prepare ions in state ñ and motional ground
state
Alice measures ion 2
Alice measures ion 1
Entire protocol requires 2.5 msec
(Murray Barrett et al., Nature 04)
Photons Bouwmeester et al., Nature (1997)
Furusawa, et al., Science (1998)
(also demonstrated at Innsbruck with ions)
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Teleportation results
ñ
A range of states was teleported
ñ - ñ
ñ - i ñ
ñ i ñ
ñ ñ
ñ

• Average fidelity 78(2)
• Best possible without entanglement 2/3

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Classical error correction

• With a noisy line, B is hard to distinguish
  from C
• A solution is to encode these letters in longer
  words
• B becomes Bravo, C becomes Charlie

Repetition code
0 000
1 111
Digitally
Send each encoded bit
Decode using majority rule
An error occurs
111
101

• Decoding or parity check allows reconstruction

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Classical error checking
Measurement result
Error action
Correction operation
None
000 or 111
No qubits flipped
Flip bit 1
100 or 011
1st bit flipped
010 or 101
Flip bit 2
2nd bit flipped
001 or 110
Flip bit 3
3rd bit flipped
Probability that more than 1 bit flips
So rep. code provides an improvement when
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Quantum error correction

• Problems in converting from classical
• Cant look at the quantum info.
• No cloning of an unknown quantum state
• Errors are continuous (not just a bit flip)
• Solution
• Use entanglement
• Make meas. that tell nothing about state (QND).

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Three bit repetition code
Encode state in three qubits via entanglement
0ñ
0ñ
Now an error E (rotation around x axis) occurs in
one of the qubits
Apply E Ä I Ä I to our state
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Three bit repetition code
Decode
Ancilla qubits
Now measure the ancilla qubits
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Error correction with rep. code
Measurement result
Syndrome
Correction operation
If we get 11ñ, we apply sX Ä I Ä I to
I Ä I Ä I
00ñ
No qubits flipped
sX Ä I Ä I
11ñ
1st qubit flipped
I Ä sX Ä I
10ñ
2nd qubit flipped
I Ä I Ä sX
01ñ
3rd qubit flipped
Correction is independent of a, b, and q
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Error correction protocol
qe
R
qe
G
G-1
qe

• G includes a three-ion entangling gate that
  gives all states but 000ñ and 111ñ a phase of p
  
• Error rotation qe applied to all qubits
• Ancilla qubits are measured after decoding
• R is either sX, sY, or I dep. on measurement

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Results

• Uncorrected infid. qe2, corrected infid. qe4
• Qubits genuinely protected for qe 1 rad.

(J. Chiaverini et al. Nature 2005)
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Summary

• Initialization and detection efficiency gt 99
• Memory coherence time gt 10 sec.
• Trapped ion qubit can be coherently manipulated,
  Fidelity gt 99.
• Two or more qubits can be deterministically
  entangled, fidelity gt 97.
• Entanglement can be distributed across different
  traps (mm).
• sympathetic cooling with 24Mg ions demonstrated
  .
• Going for more ions!

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NIST Ion Storage Group, March, 04
From left to rightJoe Britton, Jim Bergquist,
John Chiaverini, Windell Oskay, Marie Jensen,
John Bollinger, Vladislav Gerginov, Taro
Hasegawa, Carol Tanner, Wayne Itano, Jim Beall,
David Wineland, Dietrich Leibfried, Chris
Langer, Tobias Schaetz, John Jost, Roee Ozeri,
Till Rosenband, Piet Schmidt, Brad Blakestad