# Towards fault-tolerant quantum computing with trapped ions

Research paper by J. Benhelm, G. Kirchmair, C. F. Roos, R. Blatt

Indexed on: 19 Mar '08Published on: 19 Mar '08Published in: Quantum Physics

#### Abstract

Today ion traps are among the most promising physical systems for constructing a quantum device harnessing the computing power inherent in the laws of quantum physics. The standard circuit model of quantum computing requires a universal set of quantum logic gates for the implementation of arbitrary quantum operations. As in classical models of computation, quantum error correction techniques enable rectification of small imperfections in gate operations, thus allowing for perfect computation in the presence of noise. For fault-tolerant computation, it is commonly believed that error thresholds ranging between 10^-4 and 10^-2 will be required depending on the noise model and the computational overhead for realizing the quantum gates. Up to now, all experimental implementations have fallen short of these requirements. Here, we report on a Molmer-Sorensen type gate operation entangling ions with a fidelity of 99.3(1)% which together with single-qubit operations forms a universal set of quantum gates. The gate operation is performed on a pair of qubits encoded in two trapped calcium ions using a single amplitude-modulated laser beam interacting with both ions at the same time. A robust gate operation, mapping separable states onto maximally entangled states is achieved by adiabatically switching the laser-ion coupling on and off. We analyse the performance of a single gate and concatenations of up to 21 gate operations. The gate mechanism holds great promise not only for two-qubit but also for multi-qubit operations.