Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems

• URL: http://arxiv.org/abs/2405.03338v1
• Date: Mon, 6 May 2024 10:39:03 GMT
• Title: Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Authors: Yingjian Liu, Piotr Sierant, Paolo Stornati, Maciej Lewenstein, Marcin Płodzień,
• Abstract summary: Inverse Participation Ratios quantify the spread of a quantum state over a selected basis of the Hilbert space. We propose three quantum algorithms to estimate IPRs on multi-qubit and multi-qudit quantum devices.
• Score: 0.24466725954625895
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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