Enhanced thermal stability of the toric code through coupling to a bosonic bath

We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at non-zero temperature. This is achieved by locally coupling a 2D L x L toric code to a 3D bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with L. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with ln(L). For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing respectively exponentially and polynomially with L. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its low-energy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.Comment: This manuscript has some overlap with arXiv:1209.5289. However, a different model is the focus of the current work. Since this model is exactly solvable, it allows a clearer demonstration of the principle behind our quantum memory proposal. v2: minor changes and additional referenc

Effective quantum memory Hamiltonian from local two-body interactions

In [Phys. Rev. A 88, 062313 (2013)] we proposed and studied a model for a self-correcting quantum memory in which the energetic cost for introducing a defect in the memory grows without bounds as a function of system size. This positive behavior is due to attractive long-range interactions mediated by a bosonic field to which the memory is coupled. The crucial ingredients for the implementation of such a memory are the physical realization of the bosonic field as well as local five-body interactions between the stabilizer operators of the memory and the bosonic field. Here, we show that both of these ingredients appear in a low-energy effective theory of a Hamiltonian that involves only two-body interactions between neighboring spins. In particular, we consider the low-energy, long-wavelength excitations of an ordered Heisenberg ferromagnet (magnons) as a realization of the bosonic field. Furthermore, we present perturbative gadgets for generating the required five-spin operators. Our Hamiltonian involving only local two-body interactions is thus expected to exhibit self-correcting properties as long as the noise affecting it is in the regime where the effective low-energy description remains valid.Comment: 14 pages, 3 figure

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Detection of bacterial spores with lanthanide-macrocycle binary complexes

The detection of bacterial spores via dipicolinate-triggered lanthanide luminescence has been improved in terms of detection limit, stability, and susceptibility to interferents by use of lanthanide−macrocycle binary complexes. Specifically, we compared the effectiveness of Sm, Eu, Tb, and Dy complexes with the macrocycle 1,4,7,10-tetraazacyclododecane-1,7-diacetate (DO2A) to the corresponding lanthanide aquo ions. The Ln(DO2A)^+ binary complexes bind dipicolinic acid (DPA), a major constituent of bacterial spores, with greater affinity and demonstrate significant improvement in bacterial spore detection. Of the four luminescent lanthanides studied, the terbium complex exhibits the greatest dipicolinate binding affinity (100-fold greater than Tb^(3+) alone, and 10-fold greater than other Ln(DO2A)^+ complexes) and highest quantum yield. Moreover, the inclusion of DO2A extends the pH range over which Tb−DPA coordination is stable, reduces the interference of calcium ions nearly 5-fold, and mitigates phosphate interference 1000-fold compared to free terbium alone. In addition, detection of Bacillus atrophaeus bacterial spores was improved by the use of Tb(DO2A)^+, yielding a 3-fold increase in the signal-to-noise ratio over Tb^(3+). Out of the eight cases investigated, the Tb(DO2A)^+ binary complex is best for the detection of bacterial spores

Regulating Systemic Risk: Towards an Analytical Framework

The global financial crisis demonstrated the inability and unwillingness of financial market participants to safeguard the stability of the financial system. It also highlighted the enormous direct and indirect costs of addressing systemic crises after they have occurred, as opposed to attempting to prevent them from arising. Governments and international organizations are responding with measures intended to make the financial system more resilient to economic shocks, many of which will be implemented by regulatory bodies over time. These measures suffer, however, from the lack of a theoretical account of how systemic risk propagates within the financial system and why regulatory intervention is needed to disrupt it. In this Article, we address this deficiency by examining how systemic risk is transmitted. We then proceed to explain why, in the absence of regulation, market participants cannot be relied upon to disrupt or otherwise limit the transmission of systemic risk. Finally, we advance an analytical framework to inform systemic risk regulation

Bacterial Spore Detection by [Tb^(3+)(macrocycle)(dipicolinate)] Luminescence

Dipicolinic acid (DPA) is a unique constituent of bacterial spores, a dormant form of Bacillus and Clostridium, which can be detected using DPA-triggered Tb^(3+) luminescence. [Tb(DO2A)]^+ improves the sensitivity of bacterial spore detection over Tb^(3+)(aq) owing to the exclusion of coordinated water molecules and represents the first step toward construction of a DPA receptor site with enhanced binding selectivity. The title ternary [Tb(DO2A)(DPA)]- complex was structurally characterized and features two DO2A-DPA interligand hydrogen interactions that stabilize the complex