Exact and efficient Lanczos method on a quantum computer

• Published in: Quantum (Vienna, Austria) Vol. 7; p. 1018
• Main Authors: Kirby, William, Motta, Mario, Mezzacapo, Antonio
• Format: Journal Article
• Language: English
• Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 23.05.2023

We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians. While the classical Lanczos method has exponential cost in the system size to represent...