Related papers: Probabilistic quantum algorithm for Lyapunov equat…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the…
We present a method to automatically approximate moment-based invariants of probabilistic programs with non-polynomial updates of continuous state variables to accommodate more complex dynamics. Our approach leverages polynomial chaos…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
We review a family of algorithms for Lyapunov- and Riccati-type equations which are all related to each other by the idea of \emph{doubling}: they construct the iterate $Q_k = X_{2^k}$ of another naturally-arising fixed-point iteration…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times,…
The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe…
We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…
It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. In this work, we present a framework for applying a general class of non-linear functions to the amplitudes of quantum states, with…
In this paper, we give an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
In quantum operations, probabilities characterise both the degree of the success of a state transformation and, as density operator eigenvalues, the degree of mixedness of the final state. We give a unified treatment of pure-to-pure state…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…
We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in quantum machine learning by leveraging the Linear Combination of Unitaries (LCU) method. Among our investigations are quantum native…