Direct Probe of Topology and Geometry of Quantum States on IBM Q
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.
Tianqi Chen Hai-Tao Ding Ruizhe Shen Shi-Liang Zhu Jiangbin Gong