Towards fault-tolerant quantum computing with trapped ions

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.

submitted to Nature Physics

References in corpus (16)

• NMR Techniques for Quantum Control and Computation
• Quantum Computing with Very Noisy Devices
• Quantum computation with ions in thermal motion
• Multi-particle entanglement of hot trapped ions
• Fault-tolerant quantum computation with high threshold in two dimensions
• Entanglement and quantum computation with ions in thermal motion
• 'Designer atoms' for quantum metrology
• Process tomography of ion trap quantum gates
• Errors in trapped-ion quantum gates due to spontaneous photon scattering
• Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor
• Ion trap quantum gates with amplitude-modulated laser beams
• Entanglement of Trapped-Ion Clock States
• Deterministic entanglement and tomography of ion spin qubits
• Transport quantum logic gates for trapped ions
• Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+
• Improved ancilla preparation scheme increases fault-tolerant threshold

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