Related papers: Variational quantum algorithms for discovering Ham…
We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the…
Most literature in the Variational Quantum Eigensolver (VQE) algorithm focuses on finding the ground state of a physical system, by minimizing a quantum-computed cost-function. When excited states are required, the cost-function is usually…
Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
We propose a revisited variational quantum solver for linear systems, designed to circumvent the barren plateau phenomenon by combining two key techniques: adiabatic evolution and warm starts. To this end, we define an initial Hamiltonian…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonian in chemistry and physics. In this work, we first propose a Lyapunov control-inspired strategy to accelerate…
As quantum computing approaches its first commercial implementations, quantum simulation emerges as a potentially ground-breaking technology for several domains, including Biology and Chemistry. However, taking advantage of quantum…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
The variational quantum eigensolver (VQE) and its variants, which is a method for finding eigenstates and eigenenergies of a given Hamiltonian, are appealing applications of near-term quantum computers. Although the eigenenergies are…
The accurate computation of properties of large molecular systems is classically infeasible and is one of the applications in which it is hoped that quantum computers will demonstrate an advantage over classical devices. However, due to the…
Level spectroscopy stands as a powerful method for identifying the transition point that delineates distinct quantum phases. Since each quantum phase exhibits a characteristic sequence of excited states, the crossing of energy levels…
There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…
We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational…
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…