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arXiv:1408.6659 · Scientific Reports

Quantum Computation under Micromotion in a Planar Ion Crystal

S-T Wang, Chao Shen, L-M Duan

Published Feb 25, 2015• 37 citations
arXivHTMLPDF

Abstract

We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate effects: renormalization of the equilibrium positions, coupling to the transverse motional modes, and amplitude modulation in the addressing beam. We demonstrate that all of these effects can be taken into account and high-fidelity gates are possible in the presence of micromotion. This proposal opens the prospect to realize large-scale fault-tolerant quantum computation within a single Paul trap.

DOI
10.1038/srep08555

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We propose a scheme to realize scalable quantum computation in a planar ion crystal confined by a Paul trap. We show that the inevitable in-plane micromotion affects the gate design via three separate effects: renormalization of the equilibrium positions, coupling to the transverse motional modes, and amplitude modulation in the addressing beam. We demonstrate that all of these effects can be taken into account and high-fidelity gates are possible in the presence of micromotion. This proposal opens the prospect to realize large-scale fault-tolerant quantum computation within a single Paul trap.
Two- or three-dimensional Paul traps can confine a large number of ions forming a Wigner crystal, which would provide an ideal architecture for scalable quantum computation except for the micromotion, an issue that is commonly believed to be the obstacle for any high-fidelity quantum gate. Here we show that the obstacle of micromotion can be overcome with current technology, even though the magnitude of the micromotion is way outside the Lamb-Dicke region. Through exact solution of the quantum Mathieu equations, we demonstrate the principle of the gate design under micromotion using two ions in a quadrupole Paul trap as an example. The proposed micromotion quantum gates can be extended to the many-ion case and may pave a new way for scalable trapped-ion quantum computation.
The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimized in high-precision experiments such as high-fidelity quantum gates for quantum information processing (QIP). In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for QIP. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant QIP. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.
Ion trap is one of the most promising candidates for quantum computing. High-fidelity gates have been demonstrated in small ion crystals and schemes like ion shuttling have been proposed for larger systems. This thesis discusses the possibility of direct quantum computing on a large ion crystal in a Paul trap, without any shuttling of the ions. We first review a scheme to entangle two ions in a small ion crystal mediated by the collective phonon modes and analyze the gate errors. The generalization to larger systems is divided into three parts. (1) We present numerical methods to solve all the normal modes of the ion crystal, including the micromotion, up to arbitrary precision. The stability of the crystal under infinitesimal perturbation is ensured when all the normal modes have real frequencies. For finite disturbance, direct molecular dynamics simulation will be needed; after discussing some potential problems in the simulation, we give a rule of thumb for the ion crystal to be stable at a given temperature. (2) We show that when designing an entangling gate between two nearby ions, all the ions far away can be neglected, so that only a small number of normal modes are relevant. Similarly, distant entangling gates can be applied in parallel and the crosstalk is shown to decay cubically with the distance between these gates. (3) Then we present numerical methods to include the solved micromotion into the design of the entangling gates efficiently, again up to arbitrary precision. Thus we conclude that the design and the implementing of entangling gates are scalable in a large ion crystal. Finally we consider a near-term application to simulate an all-to-all coupled Ising model in a small to medium-sized ion crystal.
An ion trap is one of the most promising candidates for quantum computing. Current schemes mainly focus on a linear chain of up to about 100 ions in a Paul trap. To further scale up the qubit number, one possible direction is to use 2D or 3D ion crystals (Wigner crystals). In these systems, ions are generally subjected to large micromotion due to the strong fast-oscillating electric field, which can significantly influence the performance of entangling gates. In this paper, we develop an efficient numerical method to design high-fidelity entangling gates in a general 3D ion crystal. We present numerical algorithms to solve the equilibrium configuration of the ions and their collective normal modes. We then give a mathematical description of the micromotion and use it to generalize the gate scheme for linear ion chains into a general 3D crystal. The involved time integral of highly oscillatory functions is expanded into a fast-converging series for accurate and efficient evaluation and optimization. As a numerical example, we show a high-fidelity entangling gate design between two ions in a 100-ion crystal, with a theoretical fidelity above 99.9%.
Abstract Using a 2D ion crystal for quantum simulation and computation has been pursued for a long time. The coherent manipulation of a stationary 2D crystal in the Paul trap may be hampered by the micromotion synchronous with the oscillating electric field. Here, a simple Paul trap that stably confines over 20 ions in a stationary 2D crystal is presented. The disturbance of the micromotion in coherent operations is mitigated by making the direction of micromotion perpendicular to the transverse direction of the 2D crystal. To achieve the condition of perpendicularity, the structure of the trap electrodes is comprehensively designed, which also provides the controllability of rotating principal axes. The transverse vibrational modes by Raman laser‐beams are addressed and coherent evolution of sideband transitions on these modes observed. Moreover, this trap allows for optical access with a 0.86 numerical aperture which facilitates applying individually addressing laser‐beams. This work can be an example of realizing a 2D‐trapped‐ion based quantum simulator and computer in a Paul trap.