Related papers: Accelerated Inchworm Method with Tensor-Train Bath…
Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases.…
Recent developments in analog quantum simulators based on cold atoms and trapped ions call for cross-validating the accuracy of quantum-simulation experiments with use of quantitative numerical methods; however, it is particularly…
In general, matrix or tensor-valued functions are approximated using the method developed for vector-valued functions by transforming the matrix-valued function into vector form. This paper proposes a tensor-based interpolation method to…
We introduce a general numerical method to compute dynamics and multi-time correlations of chains of quantum systems, where each system may couple strongly to a structured environment. The method combines the process tensor formalism for…
Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of…
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…
We propose a novel algorithm for calculating the ground-state energy of quantum many-body systems by combining auxiliary-field quantum Monte Carlo (AFQMC) with tensor-train sketching. In AFQMC, a good trial wavefunction to guide the random…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…
Recent years have witnessed an increased interest in recovering dynamical laws of complex systems in a largely data-driven fashion under meaningful hypotheses. In this work, we propose a scalable and numerically robust method for this task,…
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
The simulation of open quantum systems coupled to a reservoir through multiple channels remains a substantial challenge. This kind of open quantum system arises when considering the radiationless decay of excited states that are coupled to…
The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…
In this proof-of-concept paper we show that tensor product approach is efficient for control of large quantum systems, such as Heisenberg spin wires, which are essential for emerging quantum computing technologies. We compute optimal…
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…
In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is…
Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new `Inchworm Algorithm', based on iteratively reusing information…