Related papers: The Integral Decimation Method for Quantum Dynamic…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…
The autoencoder is one of machine learning algorithms used for feature extraction by dimension reduction of input data, denoising of images, and prior learning of neural networks. At the same time, autoencoders using quantum computers are…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
Discrete integration is a fundamental problem in computer science that concerns the computation of discrete sums over exponentially large sets. Despite intense interest from researchers for over three decades, the design of scalable…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
Engineering, controlling, and simulating quantum dynamics is a strenuous task. However, these techniques are crucial to develop quantum technologies, preserve quantum properties, and engineer decoherence. Earlier results have demonstrated…
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the…
We introduce a new path integral Monte Carlo method for investigating nonadiabatic systems in thermal equilibrium and demonstrate an approach to reducing stochastic error. We derive a general path integral expression for the partition…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Two improvements with respect to previous formulations are presented for the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems. By including anharmonicities and employing a variational…
Recent advances in analog and digital quantum-simulation platforms have enabled exploration of the spectrum of entanglement Hamiltonians via variational algorithms. In this work we analyze the convergence properties of the variationally…
We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…
Dynamic Programming (DP) suffers from the well-known ``curse of dimensionality'', further exacerbated by the need to compute expectations over process noise in stochastic models. This paper presents a Monte Carlo-based sampling approach for…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Monte Carlo integration using quantum computers has been widely investigated, including applications to concrete problems. It is known that quantum algorithms based on quantum amplitude estimation (QAE) can compute an integral with a…