Quantum eigenvalue transformation for non-unitary and non-normal matrices

Quantum Scientific Computation

and Quantum Artificial Intelligence

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Organizer

Jinpeng Liu 刘锦鹏

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Speaker

Chang Liu 刘畅

Institute of Applied Physics and Computational Mathematics 北京应用物理和计算数学研究所

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Time

Tues., 16:00-17:00, Mar. 25, 2025

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Venue

Ningzhai 104

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Online

Tencent Meeting: 603-0692-7681

Quantum eigenvalue transformation for non-unitary and non-normal matrices

This talk reviews and explores recent advances in Quantum Eigenvalue Transformation (QET). We begin with a brief review of the Quantum Eigenvalue Transformation of Unitary matrices (QETU) proposed by Dong et al., which offers a new approach to ground-state preparation and energy estimation on early fault-tolerant quantum computers. Then, focusing on the work of Chan et al., we discuss extending it to non-unitary dynamics by using quantum signal processing and unitary block encoding. Next, we cover two recent improvements: the Laplace transform based method via linear combination of Hamiltonian simulation (Lap-LCHS) by An et al., and the Quantum Eigenvalue Processing framework introduced by Low and Su. By comparing their theory, complexity, and applications, we'll explore quantum algorithms' feasibility in near-term quantum hardware.

About the speaker

Chang Liu is a PhD student at the Institute of Applied Physics and Computational Mathematics.