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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.
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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
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
laser detuning Hamiltonian j n Laser field Raman Rabi freq. modes ion Motional modes
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)
1. Ion shuttling: 1. Ion shuttling: 2. Quantum networks Kielpinksi, Monroe, Wineland, Nature 417, 709 (2002) Duan, Blinov, Moehring, Monroe, 2004 Scaling it up !
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
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 (?)
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
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
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 ?
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
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
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
Optimization of the quartic trap inhomogeneity purely harmonic spacing quartic (optimized)
Gate fidelity ideal gate thermal field, T