Entanglement is recognized as a key resource for quantum computation and quantum cryptography. For quantum metrology, the use of entangled states has been discussed and demonstrated as a means of improving the signal-to-noise ratio. In addition, entangled states have been used in experiments for efficient quantum state detection and for the measurement of scattering lengths. In quantum information processing, manipulation of individual quantum bits allows for the tailored design of specific states that are insensitive to the detrimental influences of an environment. Such 'decoherence-free subspaces' (ref. 10) protect quantum information and yield significantly enhanced coherence times. Here we use a decoherence-free subspace with specifically designed entangled states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we obtain the electric quadrupole moment, which is of use for frequency standard applications. We find that entangled states are not only useful for enhancing the signal-to-noise ratio in frequency measurements--a suitably designed pair of atoms also allows clock measurements in the presence of strong technical noise. Our technique makes explicit use of non-locality as an entanglement property and provides an approach for 'designed' quantum metrology.

Gates acting on more than two qubits are appealing as they can substitute complex sequences of two-qubit gates, thus promising faster execution and higher fidelity. One important multiqubit operation is the quantum Toffoli gate that performs a controlled NOT operation on a target qubit depending on the state of two control qubits. Here we present the first experimental realization of the quantum Toffoli gate in an ion trap quantum computer, achieving a mean gate fidelity of 71(3)%. Our implementation is particularly efficient as the relevant logic information is directly encoded in the motion of the ion string.

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, 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.PACS numbers: 03.65. Wj, 03.67.Lx, 32.80.Qk Processing information with well-controlled quantum systems has the fascinating perspective of being much more powerful than classical computers for certain applications. A promising candidate for the experimental realization of quantum computing are strings of ions stored in linear Paul traps [1] as recently demonstrated by various key experiments, including the preparation of multi-particle entangled states [2,3], quantum teleportation [4,5] and quantum error correction [6]. Quantum information processing depends on the ability to implement single qubit rotations and most importantly an entangling two-qubit quantum gate [7,8,9,10]. Proper characterization and understanding of the action of gate operations and their imperfections is of vital importance in order to successfully apply them in complex computations.Generally, the implementations of quantum gates are imperfect due to decoherence and various systematic error sources present in experimental setups. A proper description of such an operation which accounts for the possibly non-unitary evolution of the qubits is provided by quantum process tomography [11,12]. Process tomography has already been applied for characterizing quantum gates in NMR and linear-optics quantum computing [13,14,15]. Here, we show that process tomography is a valuable tool for comparing different ion trap quantum gate implementations and optimizing the experimental parameters. This way, we were able to improve our controlled-NOT (CNOT) gate fidelity from 71 % [7] to almost 93 %. Moreover, the action of two successively applied gate operations is investigated and compared to the predictions from the single gate tomography result.We realize entangling gates between 40 Ca + ions held in a linear trap [16]. Quantum information is stored in superpositions of the |S ≡ S 1/2 (m = −1/2) ground state and the metastable |D ≡ D 5/2 (m = −1/2) state and is manipulated by laser pulses at a wavelength of 729 nm exciting the electric quadrupole transition between those states. A focus size smaller than the inter-ion distance and precise control of the focus position allows us to address single qubits. Detection of the qubit's quantum state is achieved by scattering light on the S 1/2 ↔ P 1/2 dipole transition and detecting the presence or absence of resonance fluorescence of t...

Absolute frequency measurement of the 40 Ca + 4s 2 S 1/2 − 3d 2 D 5/2 clock transition

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.