Related papers: State Diagrams to determine Tree Tensor Network Op…
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…
Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that…
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…
Despite the success in describing a range of quantum many-body states using tensor networks, there is a no-go theorem that rules out strictly local tensor networks as topologically nontrivial groundstates of gapped parent Hamiltonians with…
We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The…
This work studies the problem of high-dimensional data (referred to as tensors) completion from partially observed samplings. We consider that a tensor is a superposition of multiple low-rank components. In particular, each component can be…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
The simplest Tree-Tensor-States (TTS) respecting the Parity and the Time-Reversal symmetries are studied in order to describe the ground states of Long-Ranged Quantum Spin Chains with or without disorder. Explicit formulas are given for the…
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…
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent…
We prove that the ground states of a local Hamiltonian satisfy an area law and can be computed in polynomial time when the interaction graph is a tree with discrete fractal dimension $\beta<2$. This condition is met for generic trees in the…
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity measured by the quantum circuit depth…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…
Topology identification comprises reconstructing the interaction Hamiltonian of a quantum network by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology…
Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases.…
We provide an efficient approximation for the exponential of a local operator in quantum spin systems using tensor-network representations of a cluster expansion. We benchmark this cluster tensor network operator (cluster TNO) for…
TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the…
Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can…
Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…