guin-dar lin, luming duan university of michigan 2009 march meeting g.-d. lin, s.-l. zhu, r. islam,...
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Guin-Dar Lin, Luming DuanUniversity of Michigan
2009 March Meeting
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579
Guin-Dar Lin, Luming DuanUniversity of Michigan
2009 March Meeting
Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
Trapped ion quantum computation
- Monroe’s group
2S1/2
2P1/2
369 nm
|↓|↑
F,mF=0,0
F,mF=1,0
F,mF=0,0
Effective spin-1/2system in individual ion
transverseaxial
Unit:
Linear Paul trap
Motional modes modes ion
Raman Rabi freq.
laser detuning
Laser field
j n
Hamiltonian
gate time
ion controlled phaseion
phase space displacement
Quantum gate
Effective evolution
Controlled-phase flip (CPF)
Quantum control problem:
- Gate time, τ
- Laser detuning, μ
- Pulse shaping, Ω(t)
- Axial or transverse modes
~Ω(t)
1. Ion shuttling: 2. Quantum networks
BS
D1 D2
i 'i j 'j
pump pump
CNOT
pump pump
CNOT
Duan, Blinov, Moehring, Monroe, 2004
Kielpinksi, Monroe, Wineland, Nature 417, 709 (2002)
1. Ion shuttling:
Scaling it up !
- lack of translational symmetry
3. Linear chain? Adding more ions? Difficulties?
a. Geometrical issues
-- inhomogeneity:
N=20
N=60
N=120
Solution: build up a uniform ion trap Solution: build up a uniform ion trap
- structural instability
Scaling it up !
3. Linear chain? Adding more ions? Difficulties?
b. Cooling issues
c. Control issues
-- sideband cooling is difficult
-- sideband addressing is difficult
-- controlling complexityincreases with N (?)
Independent of N Independent of N
Axial Transverse
N=120
Solution: transverse modes Solution: transverse modes
Scaling it up !
Our proposalOur proposal
Box potential
finite gradient!V=0
uniform portion, F=0constant spacing=d
a real trap
+ Lowest order correction: quartic
inhomogeneity (std. deviation)
Design of a uniform ion crystal
N=120
Practical architecture
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579
gate time
ion controlled phaseion
phase space displacement
Quantum gate (control scheme)
Effective evolution
Controlled-phase flip (CPF)
Quantum control problem:
- Gate time, τ
- Laser detuning, μ
- Pulse shaping, Ω(t)
- Axial or transverse modes
2N+1 constraints
(fixed)
(fixed)
chopped into segments# =2N+1 ?
N modes: real/imaginary
Segmental pulse shaping
Answer: We don’t need 2N+1, but a few!!
Pulse shape
Infidelity
Reason:Only local motion is significant.
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579
TP
Temperature and imperfection1. Infidelity due to axial thermal motion (at Doppler temperature)
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:0901.0579
Ion spacing ~ 10 μmWidth of Gaussian beam ~ 4 μmCross-talk prob. ~ Doppler cooling is sufficient!Doppler cooling is sufficient!
G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit,
C. Monroe, L.-M. Duan arXiv:0901.0579
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.
Summary
Optimization of the quartic trap
purely harmonic
quartic (optimized)
inhomogeneity
spacing
Two central integrals
Gate fidelity
ideal gate
thermal field, T
Axial thermal fluctuation
Thank you.