Related papers: Mitigating the Hubbard Sign Problem. A Novel Appli…
We develop a systematic sign-embedding framework of operator-output quantum algorithms for matrix equations and matrix functions. Differing from the contour-integral treatment, we start with the matrix-sign embedding route: an augmented…
Projection of the Coulomb potential onto flat bands paves the way to design various interactions in the particle-hole and particle-particle channels. Here we pose the question if we can use this mapping to overcome the negative sign problem…
We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…
We study sign structures of the ground states of spin-$1/2$ magnetic systems using the methods of Boolean Fourier analysis. Previously it was shown that the sign structures of frustrated systems are of complex nature: specifically, neural…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems -- their phase transitions, ground and thermal state properties. However, in many interesting situations QMC methods…
Deep neural networks have proven to be very effective for computer vision tasks, such as image classification, object detection, and semantic segmentation -- these are primarily applied to color imagery and video. In recent years, there has…
We review the theory and applications of complex stochastic quantization to the quantum many-body problem. Along the way, we present a brief overview of a number of ideas that either ameliorate or in some cases altogether solve the sign…
We propose a framework based on the concept of the semigroup to understand the fermion sign problem. By using properties of contraction semigroups, we obtain sufficient conditions for quantum lattice fermion models to be sign-problem-free.…
In this paper, a deep neural network approach and a neuro-symbolic one are proposed for classification and regression. The neuro-symbolic predictive models based on Logic Tensor Networks are capable of discriminating and in the same time of…
A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for…
This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially relieve the sign problem in many…
Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed…
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These…
Machine learning promises to deliver powerful new approaches to neutron scattering from magnetic materials. Large scale simulations provide the means to realise this with approaches including spin-wave, Landau Lifshitz, and Monte Carlo…
Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…
We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an…