Related papers: Low-rank decomposition for quantum simulations wit…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
The performance of computational methods for many-body physics and chemistry is strongly dependent on the choice of basis used to cast the problem; hence, the search for better bases and similarity transformations is important for progress…
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of…
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…
In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
Decomposition of (finite-dimensional) operators in terms of orthogonal bases of matrices has been a standard method in quantum physics for decades. In recent years, it has become increasingly popular because of various methodologies applied…
To efficiently implement many-particle quantum simulations on quantum computers we develop and present methods for inverting the Campbell-Baker-Hausdorff lemma to 3rd and 4th order in the commutator. That is, we reexpress exp{-i(H_1 + H_2 +…
It is known that a quantum circuit may be simulated with classical hardware via stabilizer state (T-)decomposition in $O(2^{\alpha t})$ time, given $t$ non-Clifford gates and a decomposition efficiency $\alpha$. The past years have seen a…
The work discusses a new low-rank Monte Carlo technique to solve Smoluchowski-like kinetic equations. It drastically decreases the computational complexity of modeling of size-polydisperse systems. For the studied systems it can outperform…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…