Quantum algorithms for inverse participation ratio estimation in multiqubit and multiqudit systems
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 nonequilibrium properties of the system. In this work, we propose three quantum algorithms to estimate IPRs on multiqubit and multiqudit 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 multiqudit 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 Affleck-Kennedy-Lieb-Tasaki chain in a transverse field.