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

Trapped ion quantum computation - Monroe’s group 2 S 1/2 2 P 1/2 369 nm |↓|↓ |↑|↑ F,m F =0,0 F,m F =1,0 F,m F =0,0 Effective spin-1/2 system 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 phase ion 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)~Ω(t)

1. Ion shuttling:2. Quantum networks 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 - 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 complexity increases with N (?) Independent of N AxialTransverse N=120 Solution: transverse modes Scaling it up ! Our proposal

Box potential finite gradient! V=0 uniform portion, F=0 constant 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:

gate time ion controlled phase ion 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) 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: TP

Temperature and imperfection 1. 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: Ion spacing ~ 10 μm Width of Gaussian beam ~ 4 μm Cross-talk prob. ~ 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: 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.