Related papers: Efficient 2D Tensor Network Simulation of Quantum …
Projected entangled pair states (PEPS) constitute a variational family of quantum states with area-law entanglement. PEPS are particularly relevant and successful for studying ground states of spatially local Hamiltonians. However,…
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 for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the…
We present an improved version of the algorithm contracting and optimizing finite projected entangled pair states (fPEPS) in conjunction with projected entangled pair operators (PEPOs). Our work has two components to it. First, we explain…
We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
The infinite Projected Entangled Pair States (iPEPS) algorithm [J. Jordan et al, PRL 101, 250602 (2008)] has become a useful tool in the calculation of ground state properties of 2d quantum lattice systems in the thermodynamic limit.…
We systematically map low-bond-dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we demonstrate that a simulation of an $N \times M$ square-lattice PEPs network, for arbitrary $M$, of bond dimension $2$…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network…
Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with $m$ stochastically sampled $2^n$-entry quantum statevectors rather than exact $2^{2n}$-entry density matrices.…
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…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange…
An infinite projected entangled pair state (iPEPS) is a tensor network ansatz to represent a quantum state on an infinite 2D lattice whose accuracy is controlled by the bond dimension $D$. Its real, Lindbladian or imaginary time evolution…
Simulating strongly-correlated quantum many-body systems at finite temperatures is a significant challenge in computational physics. In this work, we present a scalable finite-temperature tensor network algorithm for two-dimensional quantum…
Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks…