Direct probe of topology and geometry of quantum states on the IBM Q quantum processor

Abstract

The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Although they have been investigated on various experimental platforms, to date a direct probe of the 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 reconstructed 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 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 analyzed. 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.