Related papers: Adaptive Patching for Tensor Train Computations

Network quantization is arguably one of the most practical network compression approaches for reducing the enormous resource consumption of modern deep neural networks. They usually require diverse and subtle design choices for specific…

Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive…

Operator learning for time-dependent partial differential equations (PDEs) has seen rapid progress in recent years, enabling efficient approximation of complex spatiotemporal dynamics. However, most existing methods rely on fixed time step…

The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware…

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…

Deploying deep neural networks on resource-constrained 6G edge devices demands aggressive compression with minimal accuracy loss. Quantization-Aware Training (QAT) has emerged as a leading compression approach; however, existing…

We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…

Tensor trains (TTs), also known as matrix product states (MPS), are compressed representations of high-dimensional data that can be efficiently manipulated to perform calculations on the data. In many applications, such as TT-based solvers…

Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners…

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…

In this paper, we study and implement the structural iterative eigensolvers for the large-scale eigenvalue problem in the Bethe-Salpeter equation (BSE) based on the reduced basis approach via low-rank factorizations in generating matrices,…

Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…

In this work, we firstly apply the Train-Tensor (TT) networks to construct a compact representation of the classical Multilayer Perceptron, representing a reduction of up to 95% of the coefficients. A comparative analysis between tensor…

Adaptive Rounding has emerged as an alternative to round-to-nearest (RTN) for post-training quantization by enabling cross-element error cancellation. Yet, dense and element-wise rounding matrices are prohibitively expensive for…

The efficient computation of observables beyond the total energy is a key challenge and opportunity for fault-tolerant quantum computing approaches in quantum chemistry. Here we consider the symmetry-adapted perturbation theory (SAPT)…

Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…

The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (>3) tensors. On the other hand, recently, quaternions have proven to be a very…

Density tracking by quadrature (DTQ) is a numerical procedure for computing solutions to Fokker-Planck equations that describe probability densities for stochastic differential equations (SDEs). In this paper, we extend upon existing…

Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational…

The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…