Seminar Details

Quantum circuits inherently perform linear algebra operations on quantum states, suggesting the potential for executing numerical linear algebra computations on quantum computers. However, existing quantum algorithms often rely on specific quantum access, limiting practicality. Common assumptions involve QRAM or quantum matrix oracles, yet QRAM's feasibility is uncertain. Another approach assumes a sparse Pauli decomposition, but it's not universally applicable. 
In this talk, we show an approach that assumes quantum access through state preparation circuits. We introduce State Preparation Circuits and present qMSLA, a framework operating on classical descriptions of these circuits. This framework facilitates the manipulation of quantum states represented as matrices. Each operation within qMSLA takes classical descriptions of matrix state preparation circuits as input and generates classical descriptions of new state preparation circuits, implementing matrix algebra between input matrices. Although the algorithms are classical to classical, they produce circuits intended for execution on a quantum computer.
The framework streamlines quantum algorithm construction. Instead of intricate, problem-specific designs, mathematical solutions can be translated into qMSLA operations, yielding runnable quantum circuits. This simplifies implementation, enabling straightforward quantum algorithm development.
qMSLA is demonstrated in implementing classic quantum algorithms (Hadamard Test, QFT, Phase Estimation, Qubitization, Block Encoding, etc.) and innovative algorithms like trace of matrices product. This approach paves the way for developing quantum algorithms more intuitively and accessibly.

Short bio: Liron Mor Yosef is a Ph.D. candidate in the Department of Applied Mathematics at Tel Aviv University, studying under the guidance of Prof. Haim Avron. His research focuses on the intersection of quantum computing and machine learning, with a particular emphasis on the application of randomized linear algebra techniques. Alongside his primary doctoral work, he has pursued independent side research projects focusing on the theoretical foundations of deep learning generalization and geometric frameworks for generative AI models.

Prior to his doctoral studies, he earned a B.Sc. in Mathematics and Computer Science and an M.Sc. in Applied Mathematics, graduating with honors from Tel Aviv University. His Master's research focused on developing efficient approximation algorithms to overcome computational bottlenecks in large-scale data analysis. In addition to his academic background, Liron brings practical industry experience working as an algorithm and software engineer.