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:0901.0579

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

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

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:

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

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)

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

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

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)

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

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

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 ?

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:0901.0579

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: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)

Two central integrals

Gate fidelity ideal gate thermal field, T

Axial thermal fluctuation

Universal trap structure (To be published)

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