Related papers: Relating computational complexity and quantum spec…
We study the low-lying baryon spectrum (up to 2.2 GeV) provided by experiments and different quark models using statistical tools which allow to postulate the existence of missing levels in spectra. We confirm that the experimental spectrum…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
We review the connection between statistical mechanics and the analysis of random optimization problems, with particular emphasis on the random k-SAT problem. We discuss and characterize the different phase transitions that are met in these…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
Quantum computing holds potential for accelerating the simulation of fluid dynamics. However, hardware noise in the noisy intermediate-scale quantum era significantly distorts simulation accuracy. Although error magnitudes are frequently…
We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the…
The Path Integral Monte Carlo simulated Quantum Annealing algorithm is applied to the optimization of a large hard instance of the Random 3-SAT Problem (N=10000). The dynamical behavior of the quantum and the classical annealing are…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various…
Fluctuation theorems have elevated the second law of thermodynamics to a statistical realm by establishing a connection between time-forward and time-reversal probabilities, providing invaluable insight into nonequilibrium dynamics. While…
We report a cluster of results on k-QSAT, the problem of quantum satisfiability for k-qubit projectors which generalizes classical satisfiability with k-bit clauses to the quantum setting. First we define the NP-complete problem of product…
Several basic problems of the theory of quantum phase transitions are reviewed. The effect of the quantum correlations on the phase transition properties is considered with the help of basic models of statistical physics. The effect of…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in…
We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…
Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…
This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects…