H. Häffner

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the ‘W state’ plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, ‘Greenberger–Horne–Zeilinger’ entangled states with up to six ions have been created and analysed in Boulder.

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.

Process Tomography of Ion Trap Quantum Gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

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

Realization of universal ion-trap quantum computation with decoherence-free qubits.

S_{1/2}

Robust state preparation of a single trapped ion by adiabatic passage

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Ion Trap Quantum Computing with Ca + Ions

D_{5/2}

Geometric phase gate on an optical transition for ion trap quantum computation

transition of single

Quantum information processing with trapped Ca+ ions

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

Ca