Related papers: Tensorized orbitals for computational chemistry
This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for…
In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunately they are NP-hard to compute or even approximate. Although…
We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient…
The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…
Methods for calculating an electron density of a periodic crystal constructed using non-orthogonal localised orbitals are discussed. We demonstrate that an existing method based on the matrix expansion of the inverse of the overlap matrix…
Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum…
Molecular geometry prediction of flexible molecules, or conformer search, is a long-standing challenge in computational chemistry. This task is of great importance for predicting structure-activity relationships for a wide variety of…
We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered…
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
Relativistic quintuple-zeta basis sets for the p elements are presented. The basis sets for the occupied spinors were optimized at the Dirac-Coulomb self-consistent field (SCF) level on the ground configurations. Valence and core…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a…
We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…