2024/08/14 by Yizhi Shen, Niel Van Buggenhout, Shen, Yizhi +7 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2408.07742
openalex publication_date 2024/08/14 · openalex created_date 2025/01/03 · openalex updated_date 2026/07/30
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a target operator on quantum hardware. By leveraging suitable integral representations of the operator resolvent, we show that rational transformations can be performed efficiently with Hamiltonian simulations using a linear-combination-of-unitaries (LCU). We formulate two complementary LCU approaches, discrete-time and continuous-time LCU, each providing unique strategies to decomposing the exact integral representations of a resolvent. We consider quantum rational transformation for the ubiquitous task of approximating functions of a Hermitian operator, with particular emphasis on the elementary signum function. For illustration, we discuss its application to the ground and excited state problems. Combining rational transformations with observable dynamic mode decomposition (ODMD), our recently developed noise-resilient quantum eigensolver, we design a fully real-time approach for resolving many-body spectra. Our numerical demonstration on spin systems indicates that our real-time framework is compact and achieves accurate estimation of the low-lying energies.