Direct Probe of Topology and Geometry of Quantum States on IBM Q

• URL: http://arxiv.org/abs/2403.14249v2
• Date: Thu, 6 Jun 2024 11:36:38 GMT
• Title: Direct Probe of Topology and Geometry of Quantum States on IBM Q
• Authors: Tianqi Chen, Hai-Tao Ding, Ruizhe Shen, Shi-Liang Zhu, Jiangbin Gong,
• Abstract summary: We show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. Explicit results obtained from IBM Q a Chern insulator model are presented and analysed.
• Score: 2.7801206308522417
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric properties on a universal quantum computer even for a minimum model is still in vain. In this work, we first show that a density matrix form of the quantum geometric tensor (QGT) can be explicitly re-constructed from Pauli operator measurements on a quantum circuit. We then propose two algorithms, suitable for IBM quantum computers, to directly probe QGT. The first algorithm is a variational quantum algorithm particularly suitable for Noisy Intermediate-Scale Quantum (NISQ)-era devices, whereas the second one is a pure quantum algorithm based on quantum imaginary time evolution. Explicit results obtained from IBM Q simulating a Chern insulator model are presented and analysed. Our results indicate that transmon qubit-based universal quantum computers have the potential to directly simulate and investigate topological and geometric properties of a quantum system.

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