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A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal…
We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average…
Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous-variable for simulating quantum systems at…
Neural cryptography is the application of artificial neural networks in the subject of cryptography. The functionality of this solution is based on a tree parity machine. It uses artificial neural networks to perform secure key exchange…
We introduce a new model for the task mapping problem to aid in the systematic design of algorithms for heterogeneous systems including, but not limited to, CPUs, GPUs and FPGAs. A special focus is set on the communication between the…
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
Variational quantum algorithms have been proposed to solve static and dynamic problems of closed many-body quantum systems. Here we investigate variational quantum simulation of three general types of tasks---generalised time evolution with…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…
Tangle machines are topologically inspired diagrammatic models. Their novel feature is their natural notion of equivalence. Equivalent tangle machines may differ locally, but globally they are considered to share the same information…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…