  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
$\mathcal{O}(d^2)$ for $d$ excitations on top of the previously introduced
quantum Lanczos recursion method. The formal complexity in applying all
operators to the system at once with oblivious amplitude amplification is
exponential, but this cost can be kept small to obtain the ground state by
incrementally adding operators. The error of the ground state energy based on
the accuracy of the Lanczos coefficients is investigated and the error of the
ground state energy. It is demonstrated to scale linearly with the uncertainty
of the Lanczos coefficients. Extension to non-Hermitian operators is also
discussed.
