1. 1. FOCUS and MCTP, Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 2. LQIT and ICMP, Department of Physics, South China Normal University, Guangzhou, China 3. JQI, University of Maryland and NIST, College Park, MD 20742 Guin-Dar Lin 1, S.-L. Zhu 1,2, R. Islam 3, K. Kim 3, M.-S. Chang 3, S. Korenblit 3, C. Monroe 3, and Luming Duan 1 Large-scale quantum computation in an anharmonic linear ion trap * EPL 86, 60004 (2009) Ion trap quantum computation Trapped atomic ions are believed to be one of the most promising candidates for realization of a quantum computer, due to their long- lived internal qubit coherence and strong laser-mediated Coulomb interaction. Various quantum gate protocols have been proposed and many have been demonstrated with small numbers of ions. The main challenge now is to scale up the number of trapped ion qubits to a level where the system behavior becomes intractable for any classical means. The linear rf (Paul) trap has been the workhorse for ion trap quantum computing, with atomic ions laser-cooled and confined in a 1D geometry. (Other examples include Penning traps (2D), arrays of microtraps.) Qubits are encoded in atomic internal hyperfine states, coupled to collective motional modes which serve as auxiliary channels. Working principles Main challenges in a large-scale linear ion trap (cont.)High-fidelity two-qubit gate design Architecture [1] J. I. Cirac and P. Zoller, PRL 74, 4091 (1995). [2] D. Windland et al., J. Res. NIST 103, 259 (1998). [3] A. Sorensen and K. Molmer, PRL 82, 1971 (1999); PRA 62, 022311 (2000). [4] G. J. Milburn, S. Schneider, and D. F. V. James, Fortschr. Physik 48, 801 (2000). [5] J. J. Garcia-Ripoll, P. Zoller, and J. I. Cirac, PRL 91, 157901 (2003); PRA 71, 062309 (2005). [6] S.-L. Zhu, C. Monroe, and L.-M. Duan, PRL 97, 050505 (2006); EPL 73, 485 (2006). [7] K. Kim et al., quant-ph/0905.2005 (2009). Other imperfection Pulse shape Infidelity Paul trap (Monroe’s group) |  0 1 2 0 1 2 |  P 1/2 S 1/2 12.64 GHz 369.5 nm 2 S 1/2 2 P 1/2 F=0 F=1 F=0 F=1 Qubit implementation ( 171 Yb + )Coupling spins and phonons ΔkΔk Bichromatic Raman lasers create a spin-dependent force laser detuning Laser field ion j gate time desired phase phase space displacement Hamiltonian Evolution = 0 system restored as a cycle completed Controlled-phase flip (CPF) 2. Cooling issue 3. Control issue AxialTransverse N=120 Generally speaking, side-band cooling is complicated. Better involving Doppler cooling only. Unable to resolve individual side-bands. Gate protocols must take all excitation modes into account. Controlling complexity scaling (with N) --- how the difficulty increases to design a gate? Idea: directly resolve the main challenges Build a uniform ion chain by adding anharmonic corrections to the axial potential Couple to the transverse modes: More confined. Doppler temperature required only. Controlling complexity does not increase with N: “Local” motional modes dominate. Quartic trap (lowest-order correction) N=120 excluded from computing Adjustable planar trap (Schematic) A perfect gate requires: Eliminating phonon part at the end of each cycle (N modes, real and imaginary). Acquiring the target qubit phase. 2N+1 constraints Ω1Ω1 Ω2Ω2 Ω M Chop pulse shape into M segments M=2N+1 (only required for 100% accuracy, not necessary for satisfactorily high fidelity) M=5, 6, 7…, a few (indep. of N) Systematic procedures (quadratic minimization) for gate design TP infidelity pulse shape maximum spatial displacement (Green dotted: reduced scheme) laser Two-qubit gate laser Two-qubit gate Reduced scheme frozen in space Significance of local modes Axial-motion-induced inhomogeneity of the laser field (Gaussian beam) Ion spacing δz n ~ 10 μm Width of Gaussian beam ω ~ 4 μm High-order local anharmonicity Deviation of the Lamb-Dicke Limit Main challenges in a large-scale ion trap 1. Harmonic architecture Structural instability → either increase transverse confinement or elongate axial size limit on rf trapping ion addressability problem limit on trap size coupling strength problem lack of translational symmetry → require site-dependent control N=20 N=60 N=120 Max. Min. ratio Other proposals 2. Quantum networks Duan, Blinov, Moehring, Monroe, 2004 Kielpinksi, Monroe, Wineland, Nature 417, 709 (2002) 1. Ion shuttling: J. P. Home et al., Science Express (2009) ~Ω(t)~Ω(t) shaping electrodes