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Tensor networks, particularly the tensor train (TT) format, have emerged as powerful tools for high-dimensional computations in physics and computer science. In solving coupled differential equations, such as those arising from stochastic…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
We introduce quantum circuits for simulations of multi-mode state-vectors on 3D cQED processors, using matrix product state representations. The circuits are demonstrated as applied to simulations of molecular docking based on holographic…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
Many complex chemical problems encoded in terms of physics-based models become computationally intractable for traditional numerical approaches due to their unfavourable scaling with increasing molecular size. Tensor decomposition…
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…
Large language models, like transformers, have recently demonstrated immense powers in text and image generation. This success is driven by the ability to capture long-range correlations between elements in a sequence. The same feature…
In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of…
By taking inspiration from the backflow transformation for correlated systems, we introduce a novel tensor network ansatz which extend the well-established Matrix Product State representation of a quantum-many body wave function. This new…
Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…
Since its introduction by Gauss, Matrix Algebra has facilitated understanding of scientific problems, hiding distracting details and finding more elegant and efficient ways of computational solving. Today's largest problems, which often…
Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to…
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser…
Quantum computing offers potential solutions for finding ground states in condensed-matter physics and chemistry. However, achieving effective ground state preparation is also computationally hard for arbitrary Hamiltonians. It is necessary…
We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several…
We derive a Kronecker product approximation for the micromagnetic long range interactions in a collocation framework by means of separable sinc quadrature. Evaluation of this operator for structured tensors (Canonical format, Tucker format,…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…