An Error Model for the Cirac-Zoller CNOT gate

In the framework of ion-trap quantum computing, we develop a characterization of experimentally realistic imperfections which may affect the Cirac-Zoller implementation of the CNOT gate. The CNOT operation is performed by applying a protocol of five laser pulses of appropriate frequency and polarization. The laser-pulse protocol exploits auxiliary levels, and its imperfect implementation leads to unitary as well as non-unitary errors affecting the CNOT operation. We provide a characterization of such imperfections, which are physically realistic and have never been considered before to the best of our knowledge. Our characterization shows that imperfect laser pulses unavoidably cause a leak of information from the states which alone should be transformed by the ideal gate, into the ancillary states exploited by the experimental implementation.Comment: 10 pages, 1 figure. Accepted as a contributed oral communication in the QuantumComm 2009 International Conference on Quantum Communication and Quantum Networking, Vico Equense, Italy, October 26-30, 200

Trapped ions in the strong excitation regime: ion interferometry and non--classical states

The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.Comment: 9 pages, Revtex format, 5 compressed postscript figure

Transfer of quantum states using finite resources

We discuss the problem of transfering a qubit from Alice to Bob using a noisy quantum channel and only finite resources. As the basic protocol for the transfer we apply quantum teleportation. It turns out that for a certain quality of the channel direct teleportation combined with qubit purification is superior to entanglement purification of the channel. If, however, the quality of the channel is rather low one should simply apply an estimation-preparation scheme.Comment: 9 pages RevTeX including 5 figures, replaced with revised version, to appear in Phys. Rev.

Correcting the effects of spontaneous emission on cold trapped ions

We propose two quantum error correction schemes which increase the maximum storage time for qubits in a system of cold trapped ions, using a minimal number of ancillary qubits. Both schemes consider only the errors introduced by the decoherence due to spontaneous emission from the upper levels of the ions. Continuous monitoring of the ion fluorescence is used in conjunction with selective coherent feedback to eliminate these errors immediately following spontaneous emission events, and the conditional time evolution between quantum jumps is removed by symmetrizing the quantum codewords.Comment: 19 pages; 2 figures; RevTex; The quantum codewords are extended to achieve invariance under the conditional time evolution between jump

Towards electron-electron entanglement in Penning traps

Entanglement of isolated elementary particles other than photons has not yet been achieved. We show how building blocks demonstrated with one trapped electron might be used to make a model system and method for entangling two electrons. Applications are then considered, including two-qubit gates and more precise quantum metrology protocols

Purifications of multipartite states: limitations and constructive methods

We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D; and (ii) as a purification that is written as a matrix product state of bond dimension D'. We show that these descriptions are inequivalent in the sense that D' cannot be upper bounded by D only. Then we provide two constructive methods to obtain (ii) out of (i). The sum of squares (sos) polynomial method scales exponentially in the number of different eigenvalues, and its approximate version is formulated as a semidefinite program, which gives efficient approximate purifications whose D' only depends on D. The eigenbasis method scales quadratically in the number of eigenvalues, and its approximate version is very efficient for rapidly decaying distributions of eigenvalues. Our results imply that a description of mixed states which is both efficient and locally positive semidefinite does not exist, but that good approximations do

Measurements on trapped laser-cooled ions using quantum computations

We show that a series of quantum computations involving an isolated N-quantum-bit ion register can be used to make an approximate quantum nondemolition measurement of the number state distribution of a collective vibrational mode. A unitary transformation is applied to the Fourier transformed state of the ion register to copy the vibrational statistics to the electronic mode, and the number state distribution is then measured in the electronic number state basis using the quantum jumps technique

Storing unitary operators in quantum states

We present a scheme to store unitary operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme.Comment: 4 pages, 3 figures, errors in Eq. (8) and Fig. 3 are fixed, to appear in Phys. Rev.

Adiabatic spectroscopy and a variational quantum adiabatic algorithm

Preparation of the ground state of a Hamiltonian is a problem of great significance in physics, with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long preparation times that depend on the a priori unknown spectral gap. Our work relates in a twofold way. First, we propose a method to obtain information about the spectral profile of the adiabatic evolution. Second, we present the concept of a variational quantum adiabatic algorithm (VQAA) for optimized adiabatic paths. We aim at combining the strengths of the adiabatic and the variational approaches for fast and high-fidelity ground-state preparation while keeping the number of measurements as low as possible. Our algorithms build upon ancilla protocols that we present, which allow us to directly evaluate the ground-state overlap. We benchmark for a nonintegrable spin-1/2 transverse and longitudinal Ising chain with N = 53 sites using tensor-network techniques. Using a black-box gradient-based approach, we report a reduction in the total evolution time for a given desired ground-state fidelity by a factor of 10, which makes our method suitable for the limited decoherence time of noisy-intermediate scale quantum devices.Theoretical PhysicsQuantum optics and Quantum information - OUDQuantum Matter and Optic

Sympathetic cooling of 9Be+^9Be^+ and 24Mg+^{24}Mg^+ for quantum logic

We demonstrate the cooling of a two species ion crystal consisting of one $^9Be^+$ and one $^{24}Mg^+$ ion. Since the respective cooling transitions of these two species are separated by more than 30 nm, laser manipulation of one ion has negligible effect on the other even when the ions are not individually addressed. As such this is a useful system for re-initializing the motional state in an ion trap quantum computer without affecting the qubit information. Additionally, we have found that the mass difference between ions enables a novel method for detecting and subsequently eliminating the effects of radio frequency (RF) micro-motion.Comment: Submitted to PR