1. Guin-Dar Lin, Luming Duan University of Michigan 2009 DAMOP Meeting
Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
Guin-Dar Lin, Luming Duan
University of Michigan
2009 DAMOP Meeting
Guin-Dar Lin, Luming Duan
University of Michigan
2009 DAMOP Meeting
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:

2. Trapped ion quantum computation
Linear Paul trap
- Monroe’s group

3. Trapped ion quantum computation
qubit
2S1/2
2P1/2
369 nm
|↓
|↑
F,mF=0,0
F,mF=1,0
Effective spin-1/2
system in individual ion
- Monroe’s group

4. Trapped ion quantum computation
qubit
2S1/2
2P1/2
369 nm
|↓
|↑
F,mF=0,0
F,mF=1,0
Effective spin-1/2
system in individual ion
- Monroe’s group
Motional mode spectrum
axial
transverse
Unit:

5. Hamiltonian j n Laser field laser detuning Raman Rabi freq. modes ion
(zero field on other ions)
modes
ion
Motional modes
(phonons)

6. Quantum gate ~Ω(t) Effective evolution gate time phase
phase space displacement
~Ω(t)
Quantum control problem:
- Gate time, τ
- Laser detuning, μ
- Pulse shaping, Ω(t)
- Axial or transverse modes
Controlled-phase flip
(CPF)

7. Scaling it up ! Kielpinksi, Monroe, Wineland, Nature 417, 709 (2002)
1. Ion shuttling:
1. Ion shuttling:
2. Quantum networks
Duan, Blinov, Moehring, Monroe, 2004

8. Scaling it up ! 3. Linear chain? Adding more ions? Difficulties?
I. Geometrical issues
-- inhomogeneity:
- lack of translational symmetry (optical settings, gate speed)
- structural instability
Solution: build up a uniform ion trap
N=20
N=60
N=120

9. Scaling it up ! 3. Linear chain? Adding more ions? Difficulties?
II. Cooling issues & Control issues
Our proposal
-- sideband addressing is difficult
Axial
Transverse
-- sideband cooling is difficult
(especially for axial modes)
N=120
Solution: transverse modes
(more confined and fewer phonons excited)
Only Doppler cooling is required!
-- controlling complexity
increases with N (?)
Independent of N
(Dominance of local modes)

10. Design of a uniform ion crystal
constant spacing d
Very long uniform ion lattice
F=0
Box potential
V=0
finite gradient!
a real trap
inhomogeneity (std. deviation)
+ Lowest order correction: quartic
N=120

11. Practical architecture
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:

12. Quantum gate (control scheme)
controlled phase
Effective
evolution
gate time
phase space displacement
2N+1
constraints
N modes: real/imaginary
Quantum control problem:
- Gate time, τ
- Laser detuning, μ
- Pulse shaping, Ω(t)
- Axial or transverse modes Ω1 Ω2
••• ΩM
(fixed)
(fixed)
chopped into M segments
How many? M =2N+1 ?

13. Segmental pulse shaping
Answer: We don’t need 2N+1, but a few!!
Reason:
Only “local modes” are significant.
Pulse
shape
maximal displacement during a cycle
Infidelity TP
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:

14. Temperature and imperfection
1. Infidelity due to axial thermal motion (at Doppler temperature)
Cool enough!
Cool enough!
Ion spacing ~ 10 μm
Width of Gaussian beam ~ 4 μm
Cross-talk prob. ~
2. Infidelity due to anharmonicity of the ion vibration
3. Infidelity due to transverse thermal motion (out of LD-limit correction)
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:

15. Summary
An an-harmonic axial ion trap leads to large uniform ion chains
- with translational symmetry
- structurally stable
Use of transverse phonon modes, eliminate the requirement of sideband cooling
Simple laser pulse control leads to high-fidelity gates in any large ion crystal
Complexity of quantum gate does NOT increase with the size of the system.
Multiple gates can be performed in parallel at different locations of the same ion chain.
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:

16. Optimization of the quartic trap
inhomogeneity
purely harmonic
spacing
quartic (optimized)

17. Two central integrals

18. Gate fidelity
ideal gate
thermal field, T

19. Axial thermal fluctuation

20. Universal trap structure
(To be published)

21. Universal trap structure
9 blocks of V=0 in between
(To be published)
W=30 …
V=-2
V=1
V=1
V=-2
L=100