Related papers: Quantum Simulation of Phylogenetic Trees
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
We suggest a theoretical scheme for the simulation of quantum random walks on a line using beam splitters, phase shifters and photodetectors. Our model enables us to simulate a quantum random walk with use of the wave nature of classical…
A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is…
The simple genetic algorithm is proposed for the simulation of quantum many body dynamics. It uses the selection of entangled quantum states and has the inbuilt absolute decoherence that comes from the limitation of classical memory. It…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
This work is related to the implementation of a decision tree construction algorithm on a quantum simulator. Here we consider an algorithm based on a binary criterion. Also, we study the improvement capability with quantum heuristic QAOA.…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
Probabilistic programming frameworks are powerful tools for statistical modelling and inference. They are not immediately generalisable to phylogenetic problems due to the particular computational properties of the phylogenetic tree object.…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
Many developing quantum technologies make use of quantum networks of different types. Even linear quantum networks are nontrivial, as the output photon distributions can be exponentially complex. Despite this, they can still be…
Quantum walks on binary trees are used in many quantum algorithms to achieve important speedup over classical algorithms. The formulation of this kind of algorithms as quantum circuit presents the advantage of being easily readable,…
In molecular phylogeny, relationships among organisms are reconstructed using DNA or protein sequences and are displayed as trees. A linear increase in the number of sequences results in an exponential increase of possible trees. Thus,…
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a…
Several research groups are giving special attention to quantum walks recently, because this research area have been used with success in the development of new efficient quantum algorithms. A general simulator of quantum walks is very…
In the following paper we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated to such models.…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…