Quantum information with neutral atoms as qubits

Stroboscopic generation of topological protection

Trapped neutral atoms offer a powerful route to robust simulation of complex quantum systems. We present here a stroboscopic scheme for realization of a Hamiltonian with n-body interactions on a set of neutral atoms trapped in an addressable optical lattice, using only 1- and 2-body physical operations together with a dissipative mechanism that allows thermalization to finite temperature or cooling to the ground state. We demonstrate this scheme with application to the toric code Hamiltonian, ground states of which can be used to robustly store quantum information when coupled to a low temperature reservoir.

Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian

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 gap-protected 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 or 4.8 kHz, respectively.

Atomic Fermi gas in the trimerized kagomé lattice at 2/3 filling

We study low temperature properties of a spinless interacting Fermi gas in the trimerized kagomé lattice. The case of two fermions per trimer is described by a quantum spin 1/2 model on the triangular lattice with couplings depending on the bond directions. Using exact diagonalizations we show that the system exhibits nonstandard properties of a quantum spin-liquid crystal, combining a planar antiferromagnetic order with an exceptionally large number of low-energy excitations.

Nonlinear lattice dynamics of Bose-Einstein condensates

The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop "experimental" techniques for studying nonlinear problems, continues to yield a wealth of results in the theory and applications of nonlinear Hamiltonian systems with many degrees of freedom. Inspired by the studies of this seminal model, solitary-wave dynamics in lattice dynamical systems have proven vitally important in a diverse range of physical problems-including energy relaxation in solids, denaturation of the DNA double strand, self-trapping of light in arrays of optical waveguides, and Bose-Einstein condensates (BECs) in optical lattices. BECs, in particular, due to their widely ranging and easily manipulated dynamical apparatuses-with one to three spatial dimensions, positive-to-negative tuning of the nonlinearity, one to multiple components, and numerous experimentally accessible external trapping potentials-provide one of the most fertile grounds for the analysis of solitary waves and their interactions. In this paper, we review recent research on BECs in the presence of deep periodic potentials, which can be reduced to nonlinear chains in appropriate circumstances. These reductions, in turn, exhibit many of the remarkable nonlinear structures (including solitons, intrinsic localized modes, and vortices) that lie at the heart of the nonlinear science research seeded by the FPU paradigm.

Quantum computing in the solid state: the challenge of decoherence

The current status of solid-state implementations of quantum computing is briefly described. There are numerous candidate proposals, but only comparatively recently have some of them begun to progress to the point of demonstrating coherent motion of the individual quantum bits (qubits), and the controlled coupling of more than one qubit remains a significant challenge. We also present a generalization of the fluctuation-dissipation theorem that provides a relationship between the coherent evolution entangling two spatially separated qubits, and the associated irreducible decoherence. This relationship may be used to bound the maximum attainable figures of merit in proposed two-qubit gates.

Scalable solid-state qubits: challenging decoherence and read-out

We review some basic facts about qubits and qubit processing. After a brief survey of solid-state qubits, we focus on quantized electrical circuits and superconducting qubits based on Josephson junctions. We review the general framework and indicate how the various qubits, such as the superconducting Cooper pair box charge qubit, the persistent current flux qubit, the hybrid charge-phase qubit, and the Andreev-level qubit, can be seen to appear due to different choices of design parameters. Finally, we consider multi-qubit systems and discuss some aspects of decoherence.