The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum computational class QMA [1]. In this paper we show that this important problem remains QMAcomplete when the interactions of the 2-local Hamiltonian are restricted to a two-dimensional (2-D) square lattice. Our results are partially derived with novel perturbation gadgets that employ mediator qubits which allow us to m...

The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis, for quantum states that can be realized on a cubic three-dimensional lattice. This involves a decomposition of Hilbert space into sectors transforming accordin...

Aquaporin-0 (AQP0) is the most prevalent intrinsic protein in the plasma membrane of lens fiber cells where it functions as a water selective channel and also participates in fiber-fiber adhesion. We report the 3D envelope of purified AQP0 reconstituted with random orientation in phospholipid bilayers as single particles. The envelope was obtained by combining freeze-fracture, shadowing and ran...

Quasiparticles and their interactions are a key part of our understanding quantum many-body systems. Quantum simulation experiments with cold atoms have in recent years advanced isolated quasiparticles, but so far they provided limited information regarding possible bound states. Here, we show how exploring mobile impurities immersed Bose-Einstein condensate (BEC) two-dimensional lattice can ad...

We consider the two-dimensional (2-D) (d, IC) runlengthlimited constraint and the 2-D ‘no isolated bits’ constraint (in short, the n.i.b. constraint). A binary array on the square lattice satisfies the two-dimensional (d, IC) constraint if it satisfies the one-dimensional (d, IC) constraint in both vertical and horizontal directions. Similarly, an array on the hexagonal lattice satisfies the tw...

We describe a bijection between hexagonal lattice animals and a special type of square lattice animals. Using this bijection we adopt Maple packages that automatically generates generating functions (and series expansions) for fixed square lattice lattice animals to that of fixed hexagonal animals on the two-dimensional hexagonal lattice confined to a strip 0 ≤ y ≤ k, for arbitrary k. In [Z1], ...