Related papers: Quantum Jacobi-Davidson Method
Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce…
In this paper, we explore accelerating Hamiltonian ground state energy calculation on NISQ devices. We suggest using search-based methods together with machine learning to accelerate quantum algorithms, exemplified in the Quantum…
Solving electronic structure problems is considered one of the most promising applications of quantum computing. However, due to limitations imposed by the coherence time of qubits in the Noisy Intermediate Scale Quantum (NISQ) era or the…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
The energy distribution of a quantum state is essential for accurately estimating a molecule's ground state energy in quantum computing. Directly obtaining this distribution requires full Hamiltonian diagonalization, which is…
Approximating ground and a fixed number of excited state energies, or equivalently low order Hamiltonian eigenvalues, is an important but computationally hard problem. Typically, the cost of classical deterministic algorithms grows…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
Coupling qubits together towards large-scale integration is a key point for realizing a quantum computer. We study the capacitively coupled superconducting phase qubits using two diagonalization methods, which are very efficient to obtain…
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. For various quantum algorithms, in particular in the context of quantum chemistry, it is crucial to have energy…
We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\cal H}^n |\psi\rangle$ with quantum computers, where $n$ is a nonnegative integer, $\hat{\cal H}$ is a…
Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation…
We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm…
We report an attempt to calculate energy eigenvalues of large quantum systems by the diagonalization of an effectively truncated Hamiltonian matrix. For this purpose we employ a specific way to systematically make a set of orthogonal states…
In this paper, we propose a two-level block preconditioned Jacobi-Davidson (BPJD) method for efficiently solving discrete eigenvalue problems resulting from finite element approximations of $2m$th ($m = 1, 2$) order symmetric elliptic…
Quantum computing holds immense promise for simulating quantum systems, a critical task for advancing our understanding of complex quantum phenomena. One of the primary goals in this domain is to accurately approximate the ground state of…
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov…
Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly…
The simulation of molecular electronic structure is an important application of quantum devices. Recently, it has been shown that quantum devices can be effectively combined with classical supercomputing centers in the context of the…