Related papers: Refinement of quantum Markov states on trees
Tree size ($\rm{TS}$) is an interesting measure of complexity for multiqubit states: not only is it in principle computable, but one can obtain lower bounds for it. In this way, it has been possible to identify families of states whose…
Designers of statistical machine translation (SMT) systems have begun to employ tree-structured translation models. Systems involving tree-structured translation models tend to be complex. This article aims to reduce the conceptual…
We present a bounded-error quantum algorithm for evaluating Min-Max trees. For a tree of size N our algorithm makes N^{1/2+o(1)} comparison queries, which is close to the optimal complexity for this problem.
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…
The matrix product state (MPS) is utilized to study the ground state properties and quantum phase transitions (QPTs) of the one-dimensional quantum compass model (QCM). The MPS wavefunctions are argued to be very efficient descriptions of…
In order to simulate a system of fermions on a quantum computer, it is necessary to represent the fermionic states and operators on qubits. This can be accomplished in multiple ways, including the well-known Jordan-Wigner transform, as well…
Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to…
Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
The complexity of a quantum state may be closely related to the usefulness of the state for quantum computation. We discuss this link using the tree size of a multiqubit state, a complexity measure that has two noticeable (and, so far,…
The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
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…
Quantum many-body Gibbs states satisfy an approximate local Markov property~\cite{chen2025GibbsMarkov}: local noise can be approximately recovered by a quasi-local recovery map, and the conditional mutual information decays for the…
We consider matrices with entries that are polynomials in $q$ arising from natural $q$-generalisations of two well-known formulas that count: forests on $n$ vertices with $k$ components; and trees on $n+1$ vertices where $k$ children of the…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent…
We propose a relaxation to the definition of well-structured transition systems (\WSTS) while retaining the decidability of boundedness and non-termination. In this class, the well-quasi-ordered (wqo) condition is relaxed such that it is…
A rooted tree module (RTM) $M:=M(T,F)$ over a zero-relation algebra $\Lambda:=\mathcal KQ/\langle\rho\rangle$ over a field $\mathcal K$ is given by the data of a quiver morphism $F:T\to Q$ from a rooted tree $T$ (either with a source or a…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
We introduce the quasi-ordinarization transform of a numerical semigroup. This transform will allow to organize all the semigroups of a given genus in a forest rooted at all quasi-ordinary semigroups with the given genus. This construction…