Related papers: Exact and efficient Lanczos method on a quantum co…
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…
We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator…
We report an efficient quantum algorithm for estimating the local density of states (LDOS) on a quantum computer. The LDOS describes the redistribution of energy levels of a quantum system under the influence of a perturbation. Sometimes…
The rapid progress of noisy intermediate-scale quantum (NISQ) computing underscores the need to test and evaluate new devices and applications. Quantum chemistry is a key application area for these devices, and therefore serves as an…
Accurate ground-state calculations on noisy quantum computers are fundamentally limited by restricted ansatz expressivity and unavoidable hardware errors. We introduce a hybrid-quantum classical framework that simultaneously addresses these…
In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in…
The Lanczos method with implicit restarting is one of the most popular methods for finding a few exterior eigenpairs of a large symmetric matrix $A$. Usually based on polynomial filtering, restarting is crucial to limit memory and the cost…
We consider the following constrained Rayleigh quotient optimization problem (CRQopt) $$ \min_{x\in \mathbb{R}^n} x^{T}Ax\,\,\mbox{subject to}\,\, x^{T}x=1\,\mbox{and}\,C^{T}x=b, $$ where $A$ is an $n\times n$ real symmetric matrix and $C$…
We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based…
We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
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…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
The Lanczos algorithm has proven itself to be a valuable matrix eigensolver for problems with large dimensions, up to hundreds of millions or even tens of billions. The computational cost of using any Lanczos algorithm is dominated by the…
We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements, {\em without restricting to variational ansatzes}. The lattice of size $N$ is partitioned into two subclusters. At…
We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given…
Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor…
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…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…