Non-perturbative gadget for topological quantum codes

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. Here, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians non-perturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasi-particle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other non-local spin Hamiltonians may be possible.Comment: 13 pages, 8 figures, PRL Accepte

Termite mounds harness diurnal temperature oscillations for ventilation

Many species of millimetric fungus-harvesting termites collectively build uninhabited, massive mound structures enclosing a network of broad tunnels that protrude from the ground meters above their subterranean nests. It is widely accepted that the purpose of these mounds is to give the colony a controlled microclimate in which to raise fungus and brood by managing heat, humidity, and respiratory gas exchange. Although different hypotheses such as steady and fluctuating external wind and internal metabolic heating have been proposed for ventilating the mound, the absence of direct in situ measurement of internal air flows has precluded a definitive mechanism for this critical physiological function. By measuring diurnal variations in flow through the surface conduits of the mounds of the species Odontotermes obesus, we show that a simple combination of geometry, heterogeneous thermal mass, and porosity allows the mounds to use diurnal ambient temperature oscillations for ventilation. In particular, the thin outer flutelike conduits heat up rapidly during the day relative to the deeper chimneys, pushing air up the flutes and down the chimney in a closed convection cell, with the converse situation at night. These cyclic flows in the mound flush out CO2 from the nest and ventilate the colony, in an unusual example of deriving useful work from thermal oscillations.Mathematic

Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N- representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle pre-image, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.Comment: 4 pages, 1 figur

Feedback-Induced Phase Transitions in Active Heterogeneous Conductors

An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wallbuilding) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems.Mathematic