Matrix Product States
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Related Articles from SNS
Meta Flip Graph meets Serendipitous Product: new Fast Matrix Multiplication results
Announce Type: replace Abstract: This paper presents new results for fast matrix multiplication in small formats obtained by combining the meta flip graph framework with the serendipitous product construction. The framework has been extended to support all 680 rectangular formats with dimensions up to $16 \times 16 \times 16$. Compared to the previous state of the art, ranks are improved for 207 formats. For 84 formats, ternary schemes are found where previously only integer or rational...
Meta Flip Graph meets Serendipitous Product: new Fast Matrix Multiplication results
arXiv:2606.02480v1 Announce Type: new Abstract: This paper presents new results for fast matrix multiplication in small formats obtained by combining the meta flip graph framework with the serendipitous product construction. The framework has been extended to support all 680 rectangular formats with dimensions up to $16 \times 16 \times 16$. Compared to the previous state of the art, ranks are improved for 206 formats. For 84 formats, ternary schemes are found where previously only integer...
Process-tensor approach to full counting statistics of charge transport in quantum many-body circuits
Announce Type: replace-cross Abstract: We introduce a numerical tensor-network method to compute the statistics of the charge transferred across an interface partitioning an interacting one-dimensional many-body lattice system with $U(1)$ symmetry. Our approach is based on a matrix-product state representation of the process tensor (also known as influence functional or influence matrix) describing the effect of the bulk system on the degrees of freedom at the interface, allowing us to...
Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids
Announce Type: cross Abstract: We present a new method for the efficient imaginary time evolution of quantum many-body wavefunctions represented by matrix product states (MPS). We first show that logarithmic time grids are sufficient to resolve long imaginary time dynamics, yielding an exponential reduction in the number of time steps compared with standard approaches. We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for...
Deep Tree Tensor Networks
arXiv:2502.09928v2 Announce Type: replace Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful application in natural image recognition.
Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations
Announce Type: replace Abstract: Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or matrix-product states (MPS) data encodings have emerged as a technique to systematically reduce degrees of freedom, existing formulations do not extend to complex geometries and complex flow physics. Both capabilities are offered...
Optimal Control and Dissipativity of Linear Hermitian Matrix-Valued Dynamical Systems
arXiv:2606.08856v1 Announce Type: cross Abstract: We develop a unified framework for linear-cost optimal control, finite-time optimal steering, dissipativity analysis, and zero-sum differential games for linear impulsive systems whose state is a Hermitian matrix evolving in $\mathbb{H}^{n+m}_{\succeq0}$, a class that encompasses continuous- and discrete-time linear systems and switched systems as degenerate cases, and includes the second-order moment dynamics of linear (stochastic) hybrid...
Spin Hamiltonian as Matrix-Free Linear Map
Announce Type: cross Abstract: We present an algorithm that computes the action of a generic spin Hamiltonian on a state vector on the fly, entirely avoiding explicit matrix assembly. This is achieved through mixed-radix indexing of the full tensor-product basis, which translates local spin operations into simple integer offsets. The result is an explicit framework for evaluating single- and two-site terms across arbitrary spin lattices, including mixed-spin systems.
Deterministic Monotone Min-Plus Product and Convolution
arXiv:2605.07150v2 Announce Type: replace Abstract: The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\{1,\dots,n\}$, and the goal is to compute their Min-Plus product, defined as the $n\times n$ matrix $C$ with $C_{i,j} = \min_{k}\{A_{i,k} + B_{k,j}\}$. The fastest...
Spin Correlations in Two-Particle Systems: A Pedagogically Motivated Comparison of Computational Approaches
new Abstract: In this work we present a pedagogically motivated analysis of spin-correlation calculations in a quantum system composed of two spin-$1/2$ particles. Rather than aiming at new physical results, our purpose is to clarify and bring attention to different strategies for evaluating expectation values of the form $\langle \psi | S^{(1)}_{\hat{\boldsymbol{u}}} S^{(2)}_{\hat{\boldsymbol{v}}} | \psi\rangle$, which play an important role in discussions of entanglement and Bell-type...