Related papers: Partitioned Quantum Subspace Expansion
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We introduce a diagrammatic quantum field formalism for the evaluation of normalized expectation values of operators, and suitable for systems with localized electrons. It is used to develop a convergent series expansion for the energy in…
In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…
Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies…
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs. The algorithm is employed to approximate stochastic…
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…
Krylov subspace methods are widely known as efficient algebraic methods for solving large scale linear systems. However, on massively parallel hardware the performance of these methods is typically limited by communication latency rather…
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
We propose an iterative quantum-assisted least squares (i-QLS) optimization method that leverages quantum annealing to overcome the scalability and precision limitations of prior quantum least squares approaches. Unlike traditional…
On modern large-scale parallel computers, the performance of Krylov subspace iterative methods is limited by global synchronization. This has inspired the development of $s$-step Krylov subspace method variants, in which iterations are…
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…
The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) has emerged as a promising approach for this task. However, many KQD methods…
Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device.…