相关论文: Optimization Algorithms Based on Renormalization G…

A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…

Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a…

We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work…

A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock,…

In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…

The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems…

We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…

When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU-intensive, and are useless on untractable NP-hard problems that would require thousands of…

Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…

We formulate the standard real-space renormalization group method in a way which takes into account the correlation between blocks. This is achieved in a dynamical way by means of operators which reflect the influence on a given block of…

Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum.…

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…

Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups, recently this has been relaxed in what is known as…

We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…

We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided…

Heuristic optimisers which search for an optimal configuration of variables relative to an objective function often get stuck in local optima where the algorithm is unable to find further improvement. The standard approach to circumvent…

Extremal Optimization, a recently introduced meta-heuristic for hard optimization problems, is analyzed on a simple model of jamming. The model is motivated first by the problem of finding lowest energy configurations for a disordered spin…

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which…

We propose a new Real Space Renormalization Group transformation useful for Monte Carlo calculations in theories with global or local symmetries. From relaxation arguments we define the block-spin transformation with two tunable free…