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arXiv:quant-ph/0301084 · Physical Review Letters

Quantum Computation with a One-Dimensional Optical Lattice

Jiannis K. Pachos, P. L. Knight

Published Sep 3, 2003• 148 citations
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Abstract

We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction. A realization of the Toffoli gate is presented, which requires only a single laser pulse and no individual atom addressing.

DOI
10.1103/physrevlett.91.107902

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We present an economical dynamical control scheme to perform quantum computation on a one-dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the lattice. They can be activated by external laser beams resulting in a two-qubit phase gate or in an exchange interaction. A realization of the Toffoli gate is presented, which requires only a single laser pulse and no individual atom addressing.
Optical lattices with one atom on each site and interacting via cold controlled collisions provide an efficient way to entangle a large number of qubits with high fidelity. It has already been demonstrated experimentally that this approach is especially suited for the generation of cluster states [O. Mandel et al., Nature 425, 937 (2003)] which reduce the resource requirement for quantum computing to the ability to perform single-qubit rotations and qubit read out. In this paper, we describe how to implement these rotations in one-dimensional and two-dimensional optical lattices without having to address the atoms individually with a laser field.
We propose a scheme for scalable and universal quantum computation using diatomic bits with conditional dipole-dipole interaction, trapped within an optical lattice. The qubit states are encoded by the scattering state and the bound heteronuclear molecular state of two ultracold atoms per site. The conditional dipole-dipole interaction appears between neighboring bits when they both occupy the molecular state. The realization of a universal set of quantum logic gates, which is composed of single-bit operations and a two-bit controlled-NOT gate, is presented. The readout method is also discussed.
A scheme for globally addressing a quantum computer is presented along with its realization in an optical lattice set-up of one, two or three dimensions. The required resources are mainly those necessary for performing quantum simulations of spin systems with optical lattices, circumventing the necessity for single qubit addressing. We present the control procedures, in terms of laser manipulations, required to realize universal quantum computation. Error avoidance with the help of the quantum Zeno effect is presented and a scheme for globally addressed error correction is given. The latter does not require measurements during the computation, facilitating its experimental implementation. As an illustrative example, the pulse sequence for the factorization of the number 15 is given.
We propose a scheme for implementing quantum computation with atomic ensembles on an atom chip, where a single qubit is carried by an atomic ensemble instead of a single atom. Two electronic ground states of the atoms are involved, one state with one or no atom is used to represent the qubit and the other state is used to hold the residual atoms. One and two-qubit gates are implemented by internal state transition with laser pulse sequences in the presence of the exciting blockade mechanism. A scalable quantum computer can be realized by one-dimensional or two-dimensional atomic lattices on an atom chip.
We present a model for quantum computation using nnn steady 3-level atoms kept inside a quantum cavity, or using nnn quantum-dots (QDs) kept inside a quantum cavity. In this model one external laser is pointed towards all the atoms/QDs, and nnn pairs of electrodes are addressing the atoms/QDs, so that each atom is addressed by one pair. The energy levels of each atom/QD are controlled by an external Stark field given to the atom/QD by its external pair of electrodes. Transition between two energy levels of an individual atom/ QD are controlled by the voltage on its electrodes, and by the external laser. Interactions between two atoms/ QDs are performed with the additional help of the cavity mode (using on-resonance condition). Laser frequency, cavity frequency, and energy levels are far off-resonance most of the time, and they are brought to the resonance (using the Stark effect) only at the time of operations. Steps for a controlled-NOT gate between any two atoms/QDs have been described for this model. Our model demands some challenging technological efforts, such as manufacturing single-electron QDs inside a cavity. However, it promises big advantages over other existing models which are currently implemented, and might enable a much easier scale-up, to compute with many more qubits.
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spatial wave function of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the lattice, while qubit addressability can be provided with experimentally available techniques of changing the lattice with single-site resolution. Numerical calculations show possible fidelities above 99% with gate times on the order of milliseconds.