Related papers: Improving the efficiency of variational tensor net…

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…

Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. In…

The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of…

We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…

Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the…

In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not…

Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…

Computing free energy is a fundamental problem in statistical physics. Recently, two distinct methods have been developed and have demonstrated remarkable success: the tensor-network-based contraction method and the neural-network-based…

Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

We introduce a general numerical method to compute dynamics and multi-time correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for…

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state…

Low-rank tensor compression has been proposed as a promising approach to reduce the memory and compute requirements of neural networks for their deployment on edge devices. Tensor compression reduces the number of parameters required to…

As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from…

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource…

We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we…