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Conference on Lasers and Electro-Optics

Fast quantum gates and coherent control with trapped ions

Juan José García‐Ripoll, P. Zoller, Ignacio Cirac

Published Jan 1, 2004• 0 citations
Publisher

Abstract

Trapped ions are one of the most promising systems to implement quantum computations. In fact, there seems to be no fundamental obstacle to scale-up existing set-ups [1,2]. This is achieved by moving the ions without affecting their internal state, something that has been successfully demonstrated. The current limitations of trapped ions lie in the performance of the two--qubit quantum gates which are required for universal quantum computations. In particular, the time required to perform a gate is limited by the frequency of the trap holding the ions, something which cannot be increased arbitrarily. In this work [3] we show that such a time limitation is by no means fundamental. In fact, we propose a new concept of quantum gate which is not limited by the trap frequency, is completely independent of the temperature (even beyond the Lamb-Dicke limit), and requires no addressability. We also analyze the performance of quantum gates based on this new scheme.

DOI
10.1364/iqec.2004.imc3

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Trapped ions are one of the most promising systems to implement quantum computations. In fact, there seems to be no fundamental obstacle to scale-up existing set-ups [1,2]. This is achieved by moving the ions without affecting their internal state, something that has been successfully demonstrated. The current limitations of trapped ions lie in the performance of the two--qubit quantum gates which are required for universal quantum computations. In particular, the time required to perform a gate is limited by the frequency of the trap holding the ions, something which cannot be increased arbitrarily. In this work [3] we show that such a time limitation is by no means fundamental. In fact, we propose a new concept of quantum gate which is not limited by the trap frequency, is completely independent of the temperature (even beyond the Lamb-Dicke limit), and requires no addressability. We also analyze the performance of quantum gates based on this new scheme.
Abstract We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here. We carefully study the effect of large excitation of motional mode beyond the limit of Lamb–Dicke approximation by including up to second order terms of the Lamb–Dicke parameter. We study the speed limit of multi-qubit global entangling gates without individual addressing requirements. Furthermore, our gates can be made insensitive to the fluctuation of initial motional phases which are difficult to stabilise in the phase-insensitive gate scheme.
Realising large-scale quantum computation in the near future will require increasing the number of low-error two-qubit gates that can be implemented on a quantum computer before decoherence. One of the biggest challenges facing current trapped ion quantum computers is implementing high-speed two-qubit operations, whilst increasing the number of qubits. One of the most promising proposals for overcoming current limitations is the use of ultra-fast pulses to implement fast two-qubit gates between nearest-neighbour pairs of ions. In this thesis, I investigate these ‘fast gates’ in two-dimensional arrays of microtraps, each containing a single ion. I argue that two-dimensional architectures allow for a significant reduction in the number of two-qubit gates required for a particular computation, as compared to one-dimensional ion chains. I demonstrate this reduction for a quantum simulation of a 40-mode Fermi-Hubbard Hamiltonian. I develop an efficient scheme that allows fast gates to be numerically optimised for two-dimensional geometries. I find that this optimisation scheme is capable of designing gates that are faster, higher fidelity, and require lower laser repetition rates. Using this scheme, I find that high-speed two-qubit gates can be optimised for two-dimensional architectures, with fidelities well above thresholds required for fault tolerant error correction, around 99.99%. Furthermore, I find that fast gates in these architectures are robust to the presence of large numbers of surrounding ions. Following previous studies [1, 2] which have identified pulse imperfections as a dominant source of error in fast gates, I perform a worst-case error analysis. I find the fast gates presented in this thesis to require very small errors in single-qubit rotations, and I present recommendations for achieving those requirements. I also investigate other experimental considerations, and make recommendations for overcoming other technical challenges in realising fast gates.
Trapped atomic ions are a promising medium for quantum computing, due to their long coherence times and potential for scalability. Current methods of entangling ions rely on addressing individual modes of motion within the trap and applying qubit state dependent forces with external fields. This approach can limit the speed of entangling gates and make them vulnerable to decoherence due to coupling to unwanted modes or ion heating. This thesis is directed towards demonstrating novel entanglement schemes which are not limited by the trap frequency, and can be made almost arbitrarily fast. Towards this goal, I report here on the first experiments using ultrafast laser pulses to control the internal and external states of a single trapped ion. I begin with experiments in ultrafast spin control, showing how a single laser pulse can be used to completely control both spin degrees of freedom of the ion qubit in tens of picoseconds. I also show how a train of weak pulses can be used to drive Raman transitions based on a frequency comb. I then discuss experiments using pulses to rapidly entangle the spin with the motion, and how careful spectral redistribution allows a single pulse to execute a spin-dependent momentum kick. Finally, I explain how these spin-dependent momentum kicks can be used in the future to create an ultrafast entangling gate. I go over how such a gate would work, and present experimentally realizable timing sequences which would create a maximally entangled state of two ions in a time faster than the period of motion in the trap.
Recent experiments [K. R. Brown et al., Nature (London) 471, 196 (2011); M. Harlander et al., Nature (London) 471, 200 (2011)] have demonstrated the coherent manipulations on the external vibrations of two ions, confined individually in the separated traps. Using these recently developed techniques, we propose here an approach to realize the coherent operations, e.g., the universal quantum gates, between the separated ion-trap qubits encoded by two internal atomic states of the ions. Our proposal operates beyond the usual Lamb-Dicke limits and could be applied to the scalable ion traps coupled by their vibrations.
Quantum controlled-NOT (CNOT) gates with single trapped cold ions have been experimentally demonstrated [C. Monroe et al., Phys. Rev. Lett. 75, 4714 (1995)] by using auxiliary atomic levels (besides the qubit ones) and under the usual Lamb-Dicke (LD) limit (wherein the so-called LD parameter, which represents the interaction strength between the internal and external degrees of freedom of the driven ion, is required to be sufficiently small). It has been shown [C. Monroe et al., Phys. Rev. A 55, R2489 (1997); L. F. Wei et al., 65, 062316 (2002)] that, beyond the LD limit, these gates could also be implemented for certain specific LD parameters. Here, we further show that, without any auxiliary atomic level, the desirable quantum logic gates could still be realized with sufficiently high fidelities for arbitrary LD parameters, as long as the durations of the applied laser pulses are accurately set within the decoherence times of the ions.