Related papers: Quantum Simulation of Phylogenetic Trees
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
In computer experiments, a mathematical model implemented on a computer is used to represent complex physical phenomena. These models, known as computer simulators, enable experimental study of a virtual representation of the complex…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…
Fault tree analysis is a technique widely used in risk and reliability analysis of complex engineering systems given its deductive nature and relatively simple interpretation. In a fault tree, events are usually represented by a binary…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
In this article, we propose a new approach for simulating trees, including their branches, sub-branches, and leaves. This approach combines the theory of biological development, mathematical models, and computer graphics, producing…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…
Gene gain-loss-duplication models are commonly based on continuous-time birth-death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes.…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
We present a computational model to reconstruct trees of ancestors for animals with sexual reproduction. Through a recursive algorithm combined with a random number generator, it is possible to reproduce the number of ancestors for each…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…