Related papers: Iterative Harrow-Hassidim-Lloyd quantum algorithm …
We present high-precision quantum computing simulations of three-body atoms (He, H$^-$) and molecules (H$_2^+$, HD$^+$), the latter being studied beyond the Born-Oppenheimer approximation. The Non-Iterative Disentangled Unitary Coupled…
Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
In this work, we discuss a new method for calculation of extremal eigenvectors and eigenvalues in systems or regions of parameter space where direct calculation is problematic. This technique relies on the analytic continuation of the power…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
For matrix $A$, vector $\boldsymbol{b}$ and function $f$, the computation of vector $f(A)\boldsymbol{b}$ arises in many scientific computing applications. We consider the problem of obtaining quantum state $\lvert f \rangle$ corresponding…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared…
Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the…
This article introduces a novel approach to perform the simulation of a single qubit quantum algorithm using laser beams. Leveraging the polarization states of photonic qubits, and inspired by variational quantum eigensolvers, we develop a…
We present an efficient method for preparing the initial state required by the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method can be applied when solving continuous Hermitian eigenproblems, e.g., the Schroedinger…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the Fermionic…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…