Related papers: Quantum Markov Chains on the Comb graphs: Ising mo…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
The preparation of the stationary distribution of irreducible, time-reversible Markov chains is a fundamental building block in many heuristic approaches to algorithmically hard problems. It has been conjectured that quantum analogs of…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
Recently, transformer architectures for graphs emerged as an alternative to established techniques for machine learning with graphs, such as (message-passing) graph neural networks. So far, they have shown promising empirical results, e.g.,…
Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos…
Interactive Markov chains (IMC) are compositional behavioural models extending labelled transition systems and continuous-time Markov chains. We provide a framework and algorithms for compositional verification and optimization of IMC with…
We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for…
The notion of compressed quantum computation is employed to simulate the Ising interaction of a 1D--chain consisting out of $n$ qubits using the universal IBM cloud quantum computer running on $\log(n)$ qubits. The external field parameter…
The interchange process is a random permutation model that was introduced as a way to study the quantum Heisenberg model. For this model, progress had been made on some specific graphs: trees, the hypercube, the Hamming graph, the complete…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…
We study an Ising chain undergoing a quantum phase transition in a quantum magnetic field. Such a field can be emulated by coupling the chain to a central spin initially in a superposition state. We show that - by adiabatically driving such…
Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a…
Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. The second…
In recent years, various frameworks have been proposed for the study of quantum processes with indefinite causal order. In particular, quantum circuits with quantum control of causal order (QC-QCs) form a broad class of physical supermaps…
We study the phase transitions induced by sequentially measuring a single qubit precessing under an external transverse magnetic field. Under projective quantum measurement, the probability distribution of the measurement outcomes can be…
Lattice studies of monopole condensation in QCD are based on the construction of a disorder parameter, a creation operator of monopoles which is written in terms of the gauge fields. This procedure is expected to work for any system which…
In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model…
The ground state properties of an Ising chain with nearest ($J_{1}$) and next-nearest neighbor ($J_{2}$) interactions in a transverse field are investigated using the density matrix renormalization group and cluster mean-field theory…
In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional…
We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schr\"odinger Equation on doubly-periodic metric graphs. We extend the results known for the two--dimensional square grid graph to the…