Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918022470434816 |
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| author | Liu, Yingjian Sierant, Piotr Stornati, Paolo Lewenstein, Maciej Płodzień, Marcin |
| author_facet | Liu, Yingjian Sierant, Piotr Stornati, Paolo Lewenstein, Maciej Płodzień, Marcin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems Liu, Yingjian Sierant, Piotr Stornati, Paolo Lewenstein, Maciej Płodzień, Marcin Quantum Physics Quantum Gases 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. |
| title | Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2405.03338 |