Related papers: Block-encoding based quantum algorithm for linear …
As with many tasks in engineering, structural design frequently involves navigating complex and computationally expensive problems. A prime example is the weight optimization of laminated composite materials, which to this day remains a…
One of the most promising applications of quantum computers is solving partial differential equations (PDEs). By using the Schrodingerisation technique - which converts non-conservative PDEs into Schrodinger equations - the problem can be…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less…
We present a variational quantum algorithm for structural mechanical problems, specifically addressing crack opening simulations that traditionally require extensive computational resources. Our approach provides an alternative solution for…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…
Mixed-integer linear programming problems are extensively used in industry for a wide range of optimization tasks. However, as they get larger, they present computational challenges for classical solvers within practical time limits.…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
Vector set orthogonal normalization and matrix QR decomposition are fundamental problems in matrix analysis with important applications in many fields. We know that Gram-Schmidt process is a widely used method to solve these two problems.…
Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…