Related papers: Fast Tensor Disentangling Algorithm
The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…
We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…
Quantization is commonly used in Deep Neural Networks (DNNs) to reduce the storage and computational complexity by decreasing the arithmetical precision of activations and weights, a.k.a. tensors. Efficient hardware architectures employ…
We introduce a tensor network algorithm for the solution of $p$-spin models. We show that bond compression through rank-revealing decompositions performed during the tensor network contraction resolves logical redundancies in the system…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…
Entanglement forging based variational algorithms leverage the bi-partition of quantum systems for addressing ground state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal…
We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest…
A bottleneck for analyzing the interplay between magic and entanglement is the computation of these quantities in highly entangled quantum many-body magic states. Efficient extraction of entanglement can also inform our understanding of…
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…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…
Optimization problems pose challenges across various fields. In recent years, quantum annealers have emerged as a promising platform for tackling such challenges. To provide a new perspective, we develop a heuristic tensor network (TN)…
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…