Related papers: On the comparison of optimization algorithms for t…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal…
Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems…
Neural network quantum states are a promising tool to analyze complex quantum systems given their representative power. It can however be difficult to optimize efficiently and effectively the parameters of this type of ansatz. Here we…
We investigate the application of graph-cut methods for the study of the critical behaviour of the two-dimensional random-field Ising model. We focus on exact ground-state calculations, crossing the phase boundary of the model at zero…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…
Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
An emerging trend in approximate counting is to show that certain `low-temperature' problems are easy on typical instances, despite worst-case hardness results. For the class of regular graphs one usually shows that expansion can be…
The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation…
Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…
An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…
We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow…
Solving ground states of quantum many-body systems has been a long-standing problem in condensed matter physics. Here, we propose a new unsupervised machine learning algorithm to find the ground state of a general quantum many-body system…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
In this paper we look at a class of random optimization problems that arise in the forms typically known as Hopfield models. We view two scenarios which we term as the positive Hopfield form and the negative Hopfield form. For both of these…
A new numerical method to calculate exact ground states of multi-fluxline systems with quenched disorder is presented, which is based on the minimum cost flow algorithm from combinatorial optimization. We discuss several models that can be…