Guin-Dar Lin, Luming Duan University of Michigan 2009 March Meeting

1. Large Scale Quantum Computation in an Anharmonic Linear Ion Trap Large Scale Quantum Computation in an Anharmonic Linear Ion Trap Guin-Dar Lin, Luming Duan University of Michigan 2009 March Meeting Guin-Dar Lin, Luming Duan University 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

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

3. laser detuning Hamiltonian j n Laser field Raman Rabi freq. modes ion Motional modes

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

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

6. Solution: build up a uniform ion trap Solution: build up a uniform ion trap N=20 N=60 N=120 Scaling it up ! 3. Linear chain? Adding more ions? Difficulties? a. Geometrical issues -- inhomogeneity: - lack of translational symmetry - structural instability

7. Our proposal Our proposal Solution: transverse modes Solution: transverse modes Independent of N Independent of N Scaling it up ! 3. Linear chain? Adding more ions? Difficulties? b. Cooling issues -- sideband cooling is difficult Axial Transverse c. Control issues N=120 -- sideband addressing is difficult -- controlling complexity increases with N (?)

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

9. 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

10. Controlled-phase flip (CPF) Quantum control problem: - Axial or transverse modes - Gate time,τ - Laser detuning, μ - Pulse shaping, Ω(t) Quantum gate (control scheme) Effective evolution gate time controlled phase ion ion 2N+1 constraints phase space displacement N modes: real/imaginary (fixed) (fixed) chopped into segments # =2N+1 ?

11. Segmental pulse shaping Answer: We don’t need 2N+1, but a few!! Reason: Only local motion is significant. Pulse shape Infidelity TP G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, L.-M. Duan arXiv:0901.0579

12. Doppler cooling is sufficient! Doppler cooling is sufficient! Temperature and imperfection 1. Infidelity due to axial thermal motion (at Doppler temperature) 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:0901.0579

13. 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:0901.0579

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

15. Two central integrals

16. Gate fidelity ideal gate thermal field, T

17. Axial thermal fluctuation

18. Thank you.