Speaker
Description
The field of quantum computing offers a unique opportunity to revolutionize numerical linear algebra and scientific computing. This stems from the ability of quantum computers to efficiently model complex structures, and to represent and manipulate high-dimensional vectors and matrices using exponentially fewer qubits. These advantages arise from the fundamental principles of superposition and entanglement inherent to qubits.
Yet, the current landscape of quantum computing research is dominated by intricate, tailor-made circuit designs developed in an ad-hoc manner for specific mathematical challenges. Although such state-of-the-art quantum algorithms provide a powerful means of translating diverse computations into circuits, their development is far from straightforward. It often demands extensive ``circuit engineering'' to achieve desired mathematical outcomes. This also extends to quantum numerical linear algebra.
In this talk, I will discuss our recent progress on developing a unified and systemic approach to utilizing quantum computing for numerical linear algebra. Our research centers around a novel Quantum Linear Algebra (qLA) framework offering fundamental matrix algebra building blocks, akin to BLAS -- but for Quantum Computers.