All physical implementations of quantum bits (qubits), carrying the information and computation in a putative quantum computer, have to meet the conflicting requirements of environmental decoupling while remaining manipulable through designed external signals. Proposals based on quantum optics naturally emphasize the aspect of optimal isolation [1][2][3], while those following the solid state route exploit the variability and scalability of modern nanoscale fabrication techniques [4][5][6][7][8]. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation [9][10][11], however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task. Protecting qubits from decoherence by exploiting topological stability, a qualitatively new proposal due to Kitaev [12], holds the promise for long decoherence times, but its practical physical implementation has remained unclear so far. Here, we show how strongly correlated systems developing an isolated two-fold degenerate quantum dimer liquid groundstate can be used in the construction of topologically stable qubits and discuss their implementation using Josephson junction arrays.Any quantum computer has to incorporate some fault tolerance as we cannot hope to eliminate all the various sources of decoherence. Amazing progress has been made in the development of quantum error correction schemes [13] which are based on redundant multi-qubit encoding of the quantum data combined with error detection-and recovery steps through appropriate manipulation of the data. Error correction schemes are generic (and hence are applicable to any hardware implementation), but require repeated active interference with the computer during run-time; the delocalization of the data, often in a hierarchical structure, boosts the system size by a factor 10 2 to 10 3 . Delocalization of the quantum information is also at the heart of topological quantum computing [12], however, the stabilization against decoherence is entirely deferred to the hardware level (hence it is tied to the specific implementation) and is achieved passively. In searching for a physical implementation of topological qubits one strives for an extended (many body) quantum system where the Hilbert space of quantum states decomposes into mutually orthogonal sectors, each sector remaining isolated under the action of local perturbations. Choosing the two qubit states from groundstates in different sectors protects these states from unwanted mixing through noise; protection from leakage within the sector has to be secured through a gapped excitation spectrum. As no local operator can interfere with these states, global operators must be found (and implemented) allowing for the manipulation of the qubit state.A promising candidate fulfilling the above requirements is the quantum dimer system [14][15][16]: recent quantum Monte Carlo simulations of the dimer model on a triangular lattice provide evidence for a gapped liquid ...

We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special Z Z2 Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.

We explicitly show that the Rokhsar-Kivelson dimer model on the triangular lattice is a liquid with topological order. Using the Pfaffian technique, we prove that the difference in local properties between the two topologically degenerate ground states on the cylinders and on the tori decreases exponentially with the system size. We compute the relevant correlation length and show that it equals the correlation length of the vison operator. I. RVB LIQUID AND THE ROKHSAR-KIVELSON DIMER MODELResonating valence bond (RVB) spin liquid in two dimensions is a remarkable theoretical concept which predicts very unusual low-temperature properties of spin-1/2 systems [1]. Unlike conventional magnetically-ordered ground states with spin-1 excitations, the RVB ground state has no long-range order of any local order parameter and possesses elementary excitations with spin 1/2[2]. If such a system is doped with mobile holes, the fractionalization of spin excitations translates into the effect of spin-charge separation: this scenario has been widely explored in the context of high-temperature superconductivity [2,3,4]. While a rigorous verification of the RVB liquid phase in a realistic spin system is usually very difficult due to the strongly-correlated nature of the state, many specially designed systems have confirmed RVB liquid properties [5,6,7,8,9,10].In understanding generic properties of the RVB liquid state, one may benefit from studying dimer models which are closely related to the RVB spin liquids [11,12]. In the RVB construction, the wave function is represented as a sum over singlet configurations, while in the dimer models the singlets are replaced by dimers. The difference between the spin and the dimer systems is that dimer configurations are mutually orthogonal by definition, while different singlet configurations have a finite overlap [13]. The RVB spin liquid is known to have two types of elementary excitations: spinons (spin-1/2 excitations) and visons (Z 2 vortices) [4,14]. In a dimer liquid, the spinons are prohibited by the dimer constraint (or, equivalently, are pushed infinitely high in energy), while the visons are expected to be indeed the lowest excitations above the ground state. The RVB spin liquid must have topological degeneracy on domains of nontrivial topology. Such a decoupling into topological sectors is straightforward in dimer liquids where it is defined in purely geometric terms [14,15,16]. Thus dimer models provide a convenient test ground for studying properties of RVB liquids related to vison excitations.The advantage of studying dimer models is that they are simpler than spin models, and are hence better understood and more accessible to analytical methods. The simplest dimer model contains the pair-wise hopping term and the pair-wise potential termwhere the sum is taken over the four-vertex plaquets of the lattice [15]. On the square lattice such a model has a crystal ground state (with the crystal of dimers breaking the translational symmetry of the lattice) for any ratio v/t, excep...

Basically, companies and laboratories implement production methods for their electrodes on the basis of experience, technical capabilities and commercial preferences. But how does one know whether they have ended up with the best possible electrode for the components used? What should be the (i) optimal thickness of the catalyst layer? (ii) relative amounts of electronically conducting component (catalyst, with support – if used), electrolyte and pores? (iii) “particle size distributions” in these mesophases? We may be pleased with our MEAs, but could we make them better? The details of excellently working MEA structures are typically not a subject of open discussion, also hardly anyone in the fuel cell business would like to admit that their electrodes could have been made much better. Therefore, we only rarely find (far from systematic) experimental reports on this most important issue. The message of this paper is to illustrate how strongly the MEA morphology could affect the performance and to pave the way for the development of the theory. Full analysis should address the performance at different current densities, which is possible and is partially shown in this paper, but vital trends can be demonstrated on the linear polarization resistance, the signature of electrode performance. The latter is expressed through the minimum number of key parameters characterizing the processes taking place in the MEA. Model expressions of the percolation theory can then be used to approximate the dependence on these parameters. The effects revealed are dramatic. Of course, the corresponding curves will not be reproduced literally in experiments, since these illustrations use crude expressions inspired by the theory of percolation on a regular lattice, whereas the actual mesoscopic architecture of MEA is much more complicated. However, they give us a flavour of reserves that might be released by smart MEA design.

The key factors that control the performance of perfluorinated sulfonic acid polymer electrolyte membranes cannot be deeply understood without a structural model of the material. Models of different complexity have been discussed in the literature. In this paper, we suggest a more detailed structural model of Nafion-type membranes, which results from a combined analysis of the ionomer molecular structure, data on swelling, small-angle diffraction, and conductivity as a function of water content. The analysis focuses on geometrical constraints on the self-organization of the polymer and possible patterns of phase segregation within it. The model identifies the percolation bottlenecks for proton transport and resolves controversies about the water-content dependence of the activation energy of proton mobility. It also suggests a new framework for molecular dynamics simulations of proton and water transport in such media.