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Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm…
We propose a simple graphical approach to steady state solutions of the cable equation for a general model of dendritic tree with tapering. A simple case of transient solutions is also briefly discussed.
We address unsupervised discontinuous constituency parsing, where we observe a high variance in the performance of the only previous model in the literature. We propose to build an ensemble of different runs of the existing discontinuous…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on…
For the task of subdecimeter aerial imagery segmentation, fine-grained semantic segmentation results are usually difficult to obtain because of complex remote sensing content and optical conditions. Recently, convolutional neural networks…
We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the…
Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation…
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…
The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge…
We investigate a relaxation of the notion of fractional treewidth-fragility, namely fractional tree-independence-number-fragility. In particular, we obtain polynomial-time approximation schemes for meta-problems such as finding a…
Reducing computational complexity remains a critical challenge for the widespread adoption of learning-based image compression techniques. In this work, we propose TreeNet, a novel low-complexity image compression model that leverages a…
Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space…
Quantum systems coupled to (non-)Markovian environments attract increasing attention due to their peculiar physical properties. Exciting prospects such as unconventional non-equilibrium phases beyond the Mermin-Wagner limit, or the…
A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix…
We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target…
Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose…
The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…