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Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
An efficient low-order scaling method is presented for large-scale electronic structure calculations based on the density functional theory using localized basis functions, which directly computes selected elements of the density matrix by…
We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order M\o ller-Plesset perturbation theory (MP2). In contrast to previous approximation-free MP2 codes, our implementation possesses a…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
The Random Batch Method (RBM) proposed in [Jin et al. J Comput Phys, 2020] is an efficient algorithm for simulating interacting particle systems (IPS). In this paper, we investigate the Random Batch Method with replacement (RBM-r), which is…
The fidelity estimation between two quantum states is crucial for quantum computation and information science. However, an efficacious method for this, especially for mixed states and higher-dimensional density matrices, remains elusive.…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
In this paper, a novel non-intrusive probabilistic power flow (PPF) analysis method based on the low-rank approximation (LRA) is proposed, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean,…
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, $h_{\lambda}({\bf r},{\bf r}')$, where $\lambda$ determines the interaction strength. To obtain $h_{\lambda}({\bf…
Partially observable Markov decision processes (POMDPs) is a rich mathematical framework that embraces a large class of complex sequential decision-making problems under uncertainty with limited observations. However, the complexity of…
To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
The factorized form of the unitary coupled-cluster approximation is one of the most promising methodologies to prepare trial states for strongly correlated systems within the variational quantum eigensolver framework. The factorized form of…
Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
Random phase approximation ground state contains electronic configurations where two (and more) identical electrons can occupy the same molecular spin-orbital violating the Pauli exclusion principle. This overcounting of electronic…
The predictive accuracy of popular extensions to density-functional theory (DFT) such as DFT+U and DFT plus dynamical mean-field theory (DFT+DMFT) hinges on using realistic values for the screened Coulomb interaction U. Here, we present a…
Drawing inspiration from the Lyapunov control technique for quantum systems, feedback-based quantum algorithms have been proposed for calculating the ground states of Hamiltonians. In this work, we consider extending these algorithms to…