Related papers: Improving the efficiency of variational tensor net…
Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure and are easier to optimize. However, they can be…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…
In tensor-network analysis of quantum many-body systems, it is of crucial importance to employ a tensor network with a spatial structure suitable for representing the state of interest. In the previous work [Hikihara et al., Phys. Rev.…
The computation of the ground state (i.e. the eigenvector related to the smallest eigenvalue) is an important task in the simulation of quantum many-body systems. As the dimension of the underlying vector space grows exponentially in the…
We introduce a variational Monte Carlo algorithm for approximating finite-temperature quantum many-body systems, based on the minimization of a modified free energy. This approach directly approximates the state at a fixed temperature,…
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.…
In this paper, we introduce a tensor network (TN) scheme into the entanglement augmentation process of the synergistic optimization framework by Rudolph et al. [arXiv:2208.13673] to build its process systematically for inhomogeneous…
We adapt the techniques of entanglement renormalization tensor networks to weakly interacting quantum field theories in the continuum. A key tool is "quantum circuit perturbation theory," which enables us to systematically construct…
We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes - such as quantum transport or quenches - where entanglement growth is linear…
We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By…
The multi-scale entanglement renormalisation ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on…
Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence.…