There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two dimensions. Here we show that relevant Hamiltonians can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single electron outside a closed shell of a heteronuclear molecule in its rotational ground state. Combining microwave excitation with the dipole-dipole interactions and spin-rotation couplings allows us to build a complete toolbox for effective twospin interactions with designable range and spatial anisotropy, and with coupling strengths significantly larger than relevant decoherence rates. As an illustration we discuss two models: a 2D square lattice with an energy gap providing for protected quantum memory, and another on stacked triangular lattices leading to topological quantum computing.

We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.Comment: Revised version, To appear in Phys. Rev. Lett. Three separate postscript figure

We propose a scheme for a ground-code measurement-based quantum computer, which enjoys two major advantages. First, every logical qubit is encoded in the gapped degenerate ground subspace of a spin-1 chain with nearest-neighbor two-body interactions, so that it equips built-in robustness against noise. Second, computation is processed by single-spin measurements along multiple chains dynamically coupled on demand, so as to keep teleporting only logical information into a gapprotected ground state of the residual chains after the interactions with spins to be measured are turned off. We describe implementations using trapped atoms or polar molecules in an optical lattice, where the gap is expected to be as large as 0.2 kHz or 4.8 kHz respectively. Introduction.-Reliable quantum computers require hardware with low error rates and sufficient resources to perform software-based error correction. One appealing approach to reduce the massive overhead for error correction is to process quantum information in the gapped ground states of some many-body interaction. This is the tactic used in topological quantum computation and adiabatic quantum computation. Yet, the hardware demands for the former are substantial, and the fault tolerance of the later, especially when restricted to two-body interactions, is unclear [1]. On the other hand, measurement-based quantum computation (MQC), in particular one-way computation on the 2D cluster state [2], runs by beginning with a highly entangled state dynamically generated from nearest-neighbor two-body interactions and performing computation by only single-qubit measurements and feed forward of their outcomes. However, its bare implementation may suffer decoherence of physical qubits waiting for their round of measurements in the far future, and that severely damages a prominent capability to parallelize computation. Although its fault-tolerant method by error correction has been well established [3], it is clearly advantageous if some gap-protection is provided on the hardware level.

Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.By definition, topologically ordered states [1] cannot be distinguished by local observables, i.e. there is no local order parameter. They can arise as ground states of certain Hamiltonians which have topological degeneracy and which provide robustness against noise and quasi-local perturbations. These properties of such systems are attractive for quantum memories. However, the local indistinguishability makes measuring and manipulating the topological states difficult because they are only coupled by global operations. One way to access this information is to measure properties of the low lying particlelike excitations. In two dimensions, the quasi-particles act like punctures in a surface which can have anyonic statistics and the topological properties are probed by braiding different particle types around each other. The existence of anyons also implies a topological degeneracy [2]. Quantum Hall fluids at certain filling fractions are believed to be topologically protected and there is a vigorous experimental effort to verify anyonic statistics in these systems [3]. A standard approach is to perform some kind of interferometry where one looks for non-trivial action on the fusion state space upon braiding. This is manifested as the evolution of a non-trivial statistical phase in the abelian case, or a change in the amplitude of the participating states in the non-abelian case. Some experimental evidence consistent with observation of abelian anyonic statistics in a ν = 2/5 filled Quantum Hall state has been reported [4] but an unambiguous detection of anyons is still considered an open issue [5].Spin lattice Hamiltonians can also exhibit topological order and such Hamiltonians can be built with atoms [6] or molecules [7] trapped in an optical lattice. A significant advantage of using atomic systems is that the microscopic physics is well known and there are established techniques for coherent control and measurement. Suggestions have been made for how one would design anyonic interferometers in these systems by using ...