Block Lanczos method for excited states on a quantum computer

The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is, in principle, capable of obtaining excitations, the extension to a block Lanczos routine can resolve degeneracies with better precision and only costs <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>O</a:mi><a:mo>(</a:mo><a:msup><a:mi>d</a:mi><a:mn>2</a:mn></a:msup><a:mo>)</a:mo></a:mrow></a:math> for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>d</b:mi></b:math> excitations on top of the previously introduced quantum Lanczos recursion method. Extension to non-Hermitian operators is also discussed. Published by the American Physical Society 2024