相关论文: Adaptive-weighted tree tensor networks for disorde…
Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…
Reliable detection and quantification of quantum entanglement, particularly in high-spin or many-body systems, present significant computational challenges for traditional methods. This study examines the effectiveness of ensemble machine…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
Hybrid tensor networks offer a promising route to enhance the expressivity of classical tensor network methods by incorporating quantum states prepared on a quantum computer. Existing approaches are limited by the variational optimization…
Future quantum internet relies on large-scale entanglement distribution. Quantum decoherence is a significant obstacle in large-scale networks, which otherwise perform better with multiple paths between the source and destination. We…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
The adaptive Thouless-Anderson-Palmer equation is derived for inverse Ising problems in the presence of quenched random fields. We test the proposed scheme on Sherrington-Kirkpatrick, Hopfield, and random orthogonal models and find that the…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum many-body ground state wavefunction on a lattice of size $2L$ by applying adiabatic evolution…
We consider the problem of learning underlying tree structure from noisy, mixed data obtained from a linear model. To achieve this, we use the expectation maximization algorithm combined with Chow-Liu minimum spanning tree algorithm. This…
In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman…
We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair…
We introduce scalable machine learning models to accurately predict two key quantum transport properties, the transmission coefficient T(E) and average local density of states (Average-LDOS) in two-dimensional (2D) hexagonal materials with…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…