Large-scale quantum computation in an anharmonic linear ion trap

Abstract

We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses.PACS numbers: 03.67. Lx, 32.80.Qk, 03.67.Pp Trapped atomic ions remain one of the most attractive candidates for the realization of a quantum computer, owing to their long-lived internal qubit coherence and strong laser-mediated Coulomb interaction [1,2,3,4]. Various quantum gate protocols have been proposed [1,5,6,7,8,9] and many have been demonstrated with small numbers of ions [4,10,11,12,13,14]. The central challenge now is to scale up the number of trapped ion qubits to a level where the quantum behavior of the system cannot be efficiently modeled through classical means [4]. The linear rf (Paul) trap has been the workhorse for ion trap quantum computing, with atomic ions laser-cooled and confined in 1D crystals [1,2,3,4] (although there are proposals for the use of 2D crystals in a Penning trap [15] or array of microtraps [6]). However, scaling the linear ion trap to interesting numbers of ions poses significant difficulties [2,4]. As more ions are added to a harmonic axial potential, a structural instability causes the linear chain to buckle near the middle into a zigzag shape [16], and the resulting low-frequency transverse modes and the off-axis rf micromotion of the ions makes gate operation unreliable and noisy. Even in a linear chain, the complex motional mode spectrum of many ions makes it difficult to resolve individual modes for quantum gate operations, and to sufficiently laser cool many low-frequency modes. One promising approach is to operate with small linear ion chains and multiplex the system by shuttling ions between multiple chains through a maze of trapping zones, but this requires complicated electrode structures and exquisite control of ion trajectories [2,17].In this paper, we propose a new approach to ion quantum computation in a large linear architecture that circumvents the above difficulties. This scheme is based on combination of several ideas. First, an anharmonic axial trap provided by static electrode potentials can stabilize a single linear crystal containing a large number of ions. Second, tightly-confined and closely-spaced transverse phonon modes can mediate quantum gate operations in a large architecture [18], while eliminating the need for single-mode resolution and multimode sideband cooling. Third, gate operations on the large ion array exploit the local character of the laser-induced dipole interaction that is dominated by nearby ions only. As a result, the complexity of the quantum gate does not increase with the size of the system.The proposed ion architecture is illustrated in Fig. 1. It is a large linear array where the strong confi...

Sympathetic cooling in a large ion crystal

“…1 we show the distribution of δx i and δz i in a harmonic trap for both the axial and transverse motion at the Doppler temperature T D , and their contribution to the corresponding gate infidelities [29]. In this case, the axial fluctuation δz i varies in space, suggesting that the longitudinal motion of the whole ion chain is "more collective" and relies on the global geometry.…”

“…For a small crystal, the axial confinement is usually approximated by V (z) = 1 2 mω 2 z z 2 with ω z ≪ ω x so that the one dimensional alignment is stabilized. For a large crystal, the axial potential might take an anharmonic form [29]. Trapped ions have collective motion around their classical equilibrium positions.…”

“…For trapped ion quantum computing, the computational fidelity is determined by the ion PF δx ξ i ≡ x ξ2 i (denoted by δx i and δz i for transverse and axial motion, respectively). When the quantum gate is operated by means of the transverse modes, the estimated infidelity is δF x i ∼ π 2 η 4 i /4 [3,29,30], where the Lamb-Dicke parameter η i ∼ |∆k| δx i with ∆k x the wavevector difference of the two Raman beams. Another possible source of error comes from the spatial non-uniformity of the laser intensity when a single beam addresses a specific ion; the ion's axial motion results in variation of the actual Rabi frequency.…”

“…Another possible source of error comes from the spatial non-uniformity of the laser intensity when a single beam addresses a specific ion; the ion's axial motion results in variation of the actual Rabi frequency. This error is estimated by δF z i ∼ π 2 (δz i /w) 4 /2 given that the laser beam's Rabi frequency is approximated by a Gaussian profile Ω(z) ∝ e −((z−z 0 i )/w) 2 with width w [29]. Both of the gate errors are determined by the position thermal fluctuation δx i or δz i of the ions.…”

“…The ions may be subjected to further sub-Doppler cooling, such as sideband cooling. However, the difficulty of sideband cooling scales up with the number of phonon modes, which increase with the number of ions [27][28][29]. It has been shown that in principle high-fidelity quantum computation can be achieved even at the Doppler temperature by employing the ions' transverse phonon modes [29,30].…”