Related papers: Universal computation with limited resources: Belo…
High-performance graphical processing units (GPU) are used for the repeated parallelised propagation of non-linear partial differential equations on large spatio-temporal grids. The main challenge results as a combination of the requirement…
In this paper we explore the power of geometry to overcome the limitations of non-cooperative self-assembly. We define a generalization of the abstract Tile Assembly Model (aTAM), such that a tile system consists of a collection of…
We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a…
In the present work we will present and analyze some basic processes at the local and global level in linguistic derivations that seem to go beyond the limits of Markovian or Turing-like computation, and require, in our opinion, a quantum…
We develop techniques to capture the effect of transport on the long-term dynamics of small, localized initial data in nonlinearly coupled reaction-diffusion-advection equations on the real line. It is well-known that quadratic or cubic…
In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle…
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
Informational contributions to thermodynamics can be studied in isolation by considering systems with fully-degenerate Hamiltonians. In this regime, being in non-equilibrium -- termed informational non-equilibrium -- provides thermodynamic…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build…
An intriguing interpretation of the time-evolution of dynamical systems is to view it as a computation that transforms an initial state to a final one. This paradigm has been explored in discrete systems such as cellular automata models,…
This paper formally proposes a problem about the efficient utilization of the four dimensional space-time. Given a cuboid container, a finite number of rigid cuboid items, and the time length that each item should be continuous baked in the…
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different…
Magic is the resource that quantifies the amount of beyond-Clifford operations necessary for universal quantum computing. It bounds the cost of classically simulating quantum systems via stabilizer circuits central to quantum error…
System and synthetic biology are rapidly evolving systems, but both lack tools such as those used in engineering environments to shift the their focus from the design of parts (details) to the design of systems (behaviors); to aggravate,…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
This paper considers a network of collaborating agents for local resource allocation subject to nonlinear model constraints. In many applications, it is required (or desirable) that the solution be anytime feasible in terms of satisfying…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…