S. Gulde

Realization of the Cirac-Zoller controlled-NOT quantum gate.

Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac–Zoller proposal for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac–Zoller proposal. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams; the qubits are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.

Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch–Jozsa algorithm) requires just one examination step. The Deutsch–Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch–Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.

How to realize a universal quantum gate with trapped ions

We report the realization of an elementary quantum processor based on a linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to store the quantum information in long lived electronic states. We present the realization of single-qubit and of universal two-qubit logic gates. The two-qubit operation relies on the coupling of the ions through their collective quantized motion. A detailed description of the setup and the methods is included.

The coherence of qubits based on single Ca+ ions

Two-level ionic systems, where quantum information is encoded in long lived states (qubits), are discussed extensively for quantum information processing. We present a collection of measurements which characterize the stability of a qubit based on the

Sympathetic ground-state cooling and coherent manipulation with two-ion crystals

S_{1/2}

Ground state cooling, quantum state engineering and study of decoherence of ions in Paul traps

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Quantum information processing with trapped Ca+ ions

D_{5/2}

Quantum information processing and cavity QED experiments with trapped Ca' ions

transition of single

Towards quantum information with trapped calcium ions

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Bell States of Atoms with Ultralong Lifetimes and Their Tomographic State Analysis

Ca