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Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
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…
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of…
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit…
Space-time dependence of imaginary-time propagators, vital for \textit{ab initio} and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X {\bf 13},…
Homogenization in terms of multiscale limits transforms a multiscale problem with $n+1$ asymptotically separated microscales posed on a physical domain $D \subset \mathbb{R}^d$ into a one-scale problem posed on a product domain of dimension…
The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess…
Numerically exact simulations of quantum reaction dynamics, including non-adiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of…
We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…
We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
Although considerable progress has been obtained in neural network quantization for efficient inference, existing methods are not scalable to heterogeneous devices as one dedicated model needs to be trained, transmitted, and stored for one…
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…
Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit…
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network…
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 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…
Neural quantum states (NQS) are powerful ans\"atze in the variational Monte Carlo framework, yet their architectures are often treated as black boxes. We propose a physically transparent framework in which NQS are treated as neural…