Related papers: Optimizing and Comparing Quantum Resources of Stat…
A major thrust in quantum algorithm development over the past decade has been the search for the quantum algorithms that will deliver practical quantum advantage first. Today's quantum computers - and even early fault-tolerant quantum…
The VQE algorithm has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, we introduce Quantum Sampling Regression (QSR), an alternative…
In recent years two Krylov subspace methods have been proposed for solving skew symmetric linear systems, one based on the minimum residual condition, the other on the Galerkin condition. We give new, algorithm-independent proofs that in…
We develop a paradigm for building quantum models in the orthonormal space of Chebyshev polynomials. We show how to encode data into quantum states with amplitudes being Chebyshev polynomials with degree growing exponentially in the system…
The nearest neighbor spacing distribution (NNSD) is one of common methods in statistical analysis of nuclear energy levels. In this paper, we have proposed Maximum Likelihood Estimation (MLE) method to evaluate parameter of (NNSD)'s which…
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-based learning algorithms. This is different if the…
We propose a quantum error correction protocol for continuous-variable finite-energy, approximate Gottesman-Kitaev-Preskill (GKP) states undergoing small Gaussian random displacement errors, based on the scheme of Glancy and Knill [Phys.…
Simulating complex spin systems, known for high frustration and entanglement, presents significant challenges due to their intricate energy landscapes. This study focuses on the $J_{1}-J_{2}$ Heisenberg model, renowned for its rich phase…
The Gradient Ascent Pulse Engineering (GRAPE) is a celebrated control algorithm with excellent converging rates, owing to a piece-wise-constant ansatz for the control function that allows for cheap objective gradients. However, the…
Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. To accommodate the diverse characteristics of quantum chemical systems,…
We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high-energy QCD. In particular, we observe that the cascade…
We introduce and employ two QM:QM schemes (a quantum mechanical method embedded into another quantum mechanical method) and report their performance for the X23 set of molecular crystals. We furthermore present the theory to calculate the…
We simulate the Lipkin-Meshkov-Glick (LMG) model using the Variational-Quantum-Eigensolver (VQE) algorithm on a neutral atom quantum computer. We test the ground-state energy of spin systems with up to 15 spins. Two different encoding…
Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics,…
While numerical simulations are presented in most papers introducing new methods to enhance the VQE performance, comprehensive, comparative, and applied studies remain relatively rare. We present a comprehensive, yet concise guide for the…
Quantum computing shows promise for addressing computationally intensive problems but is constrained by the exponential resource requirements of general quantum state tomography (QST), which fully characterizes quantum states through…
By adding a non-linear core correction to the well established Dual Space Gaussian type pseudopotentials for the chemical elements up to the third period, we construct improved pseudopotentials for the Perdew Burke Ernzerhof (PBE)…
The study and prediction of chemical reactivity is one of the most important application areas of molecular quantum chemistry. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying…
Two self-consistent schemes involving Hedin's $GW$ approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent $GW$ approximation (SC$GW$) and the quasi-particle…
The task of estimating the ground state of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for…