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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…
In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand side term is a selfadjoint, continuous and coercive…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
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.…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is…
A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Estimating observable expectation values in eigenstates of quantum systems has a broad range of applications and is an area where early fault-tolerant quantum computers may provide practical quantum advantage. We develop a hybrid…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
Solving Hamiltonian matrix is a central task in quantum many-body physics and quantum chemistry. Here we propose a novel quantum algorithm named as a quantum Heaviside eigen solver to calculate both the eigen values and eigen states of the…
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum…