相关论文: An alternative implementation of the Lanczos algor…

Recently, artificial intelligence for science has made significant inroads into various fields of natural science research. In the field of quantum many-body computation, researchers have developed numerous ground state solvers based on…

Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and…

This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…

Objectives involving bilinear forms $u^\top f(A(\theta))v$ for Hermitian $A$ arise widely in scientific computing and probabilistic machine learning. For large matrices, Lanczos efficiently approximates these quantities, but differentiating…

Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…

Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious…

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…

This paper describes how to propagate wavefields for arbitrary numbers of traditional time steps in a single step, called a superstep. We show how to construct operators that accomplish this task for finite-difference time domain schemes,…

A stochastic approach to the quantum dynamics randomly modulated in time by a discrete state non-Markovian noise, which possesses an arbitrary non-exponential distribution of the residence times, is developed. The formally exact expression…

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 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…

We propose a general-purpose, self-adaptive approach to construct variational wavefunction ans\"atze for highly accurate quantum dynamics simulations based on McLachlan's variational principle. The key idea is to dynamically expand the…

In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…

Quantum state transfer is a key operation for quantum information processing. The original pitch-and-catch protocols rely on flying qubits or single photons with engineered wavepacket shapes to achieve a deterministic, fast and…

Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…

Quantum state diffusion shows how stochastic interaction with the environment may cause localisation of the wave-function, and thereby demonstrates that quantum mechanics need not invoke a separate axiom of measurement to explain the…

Parameterized quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational…

We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and…

Reliable transmission of quantum optical states through real-world environments is key for quantum communication and imaging. Yet, aberrations and scattering in the propagation path can scramble the transmitted signal and hinder its use. A…