相关论文: Novel linear algebraic theory and one-hundred-mill…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We develop K$\omega$, an open-source linear algebra library for the shifted Krylov subspace methods. The methods solve a set of shifted linear equations $(z_k I-H)x^{(k)}=b\, (k=0,1,2,...)$ for a given matrix $H$ and a vector $b$,…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Quantum subspace diagonalization and quantum Krylov algorithms offer a feasible, pre- or early-fault tolerant alternative to quantum phase estimation for using quantum computers to estimate the low-lying spectra of quantum systems. However,…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that…
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
The Vlasov-Maxwell system of equations, which describes classical plasma physics, is extremely challenging to solve, even by numerical simulation on powerful computers. By linearizing and assuming a Maxwellian background distribution…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
Powerful generative artificial intelligence from large language models (LLMs) harnesses extensive computational resources for inference. In this work, we investigate the transformer architecture, a key component of these models, under the…