  Inverse Participation Ratios (IPRs) and the related Participation Entropies
quantify the spread of a quantum state over a selected basis of the Hilbert
space, offering insights into the equilibrium and non-equilibrium properties of
the system. In this work, we propose three quantum algorithms to estimate IPRs
on multi-qubit and multi-qudit quantum devices. The first algorithm allows for
the estimation of IPRs in the computational basis by single-qubit measurements,
while the second one enables measurement of IPR in the eigenbasis of a selected
Hamiltonian, without the knowledge about the eigenstates of the system. Next,
we provide an algorithm for IPR in the computational basis for a multi-qudit
system. We discuss resources required by the algorithms and benchmark them by
investigating the one-axis twisting protocol, the thermalization in a deformed
PXP model, and the ground state of a spin-$1$ AKLT chain in a transverse field.
