Analyzing quadratic unconstrained binary optimization problems via multicommodity flows

Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n{0,1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C₂,C₃,C₄,…. It is known that C₂ can be computed by solving a maximum flow problem, whereas the only previously known algorithms for computing require solving a linear program. In this paper we prove that C₃ can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0,1}ⁿ, this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.     

Braid group, gauge invariance, and topological order

Topological order in two-dimensional systems is studied by combining the braid group formalism with a gauge invariance analysis. We show that flux insertions (or large gauge transformations) pertinent to the toroidal topology induce automorphisms of the braid group, giving rise to a unified algebraic structure that characterizes the ground-state subspace and fractionally charged, anyonic quasiparticles. Minimal ground-state degeneracy is derived without assuming any relation between quasiparticle charge and statistics. We also point out that noncommutativity between large gauge transformations is essential for the topological order in the fractional quantum Hall effect.     

Experimental test of two-way quantum key distribution in the presence of controlled noise

We describe the experimental test of a quantum key distribution performed with a two-way protocol without using entanglement. An individual incoherent eavesdropping is simulated and induces a variable amount of noise on the communication channel. This allows a direct verification of the agreement between theory and practice.     

New critical frontiers for the potts and percolation models

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.     

Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies

A one-dimensional magnetic plasmon propagating in a linear chain of single split ring resonators is proposed. The subwavelength size resonators interact mainly through exchange of conduction current, resulting in stronger coupling as compared to the corresponding magneto-inductive interaction. Finite-difference time-domain simulations in conjunction with a developed analytical theory show that efficient energy transfer with signal attenuation of less then 0.57 dB/microm and group velocity higher than 1/4c can be achieved. The proposed novel mechanism of energy transport in the nanoscale has potential applications in subwavelength transmission lines for a wide range of integrated optical devices.     

Observation of the first-order transition in ultrafiltration of flexible linear polymer chains

Using a special double-layer membrane to avoid interaction among flow fields generated by different pores, we have, for the first time, observed the predicted discontinuous first-order transition in ultrafiltration of flexible linear polymer chains. Namely, the chain could pass through a pore much smaller than its unperturbed radius only when the flow rate is higher than a certain value. When only one chain and one pore are considered in theory, such a threshold is surprisingly independent of both the chain length and the pore size. Our results reveal that for a membrane with many pores and at a microscopic flow rate () lower than the threshold, the inevitable blocking of some pores by longer nonstretched coiled chains increases in those unblocked pores because the macroscopic flow rate () is a constant. Long chains have two populations, coiled and stretched, in a real ultrafiltration experiment when is lower than the threshold.     

Commutability between the semiclassical and adiabatic limits

We study the adiabatic limit and the semiclassical limit with a second-quantized two-mode model of a many-boson interacting system. When its mean-field interaction is small, these two limits are commutable. However, when the interaction is strong and over a critical value, the two limits become incommutable. This change of commutability is associated with a topological change in the structure of the energy bands. These results reveal that nonlinear mean-field theories, such as Gross-Pitaevskii equations for Bose-Einstein condensates, can be invalid in the adiabatic limit.