Related papers: Simultaneous state-time approximation of the chemi…
Quantum computing holds promise for revolutionizing computational chemistry simulations, particularly in drug discovery. However, current quantum hardware is limited by noise and scale, necessitating bridging technologies. This study…
In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…
We derive rank bounds on the quantized tensor train (QTT) compressed approximation of singularly perturbed reaction diffusion partial differential equations (PDEs) in one dimension. Specifically, we show that, independently of the scale of…
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…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which…
With the rapid advancement of Transformer-based Large Language Models (LLMs), generative recommendation has shown great potential in enhancing both the accuracy and semantic understanding of modern recommender systems. Compared to LLMs, the…
A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical…
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states…
Path-integral techniques are a powerful tool used in open quantum systems to provide an exact solution for the non-Markovian dynamics. However, the exponential scaling of the tensor size with quantum memory length of these techniques limits…
Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…
We consider the solution of linear systems with tensor product structure using a GMRES algorithm. In order to cope with the computational complexity in large dimension both in terms of floating point operations and memory requirement, our…
We demonstrate that a tensor product structure could be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using classical fields modulated with pseudorandom phase sequences, we discuss…
Simulation of conditional master equations is important to describe systems under continuous measurement and for the design of control strategies in quantum systems. For large bosonic systems, such as BEC and atom lasers, full quantum field…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
Neural network quantum states (NQS) have emerged as a powerful and flexible framework for addressing quantum many-body problems. While successful for model Hamiltonians, their application to molecular systems remains challenging for several…
Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables…
This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will…
We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, we discuss…