Finite-Size Scaling on a Digital Quantum Simulator using Quantum Restricted Boltzmann Machine

Abstract

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occuring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic 1

Quantum machine learning for chemistry and physics

“…The critical point and the critical exponents for a quantum phase transition can be determined using a QML approach through the finite-size scaling (FSS) analysis. 734 Therefore, the development of QML approaches has a huge role to play in the coming years in the domain of electronic structure, materials, and property prediction methods. Similar statements can also be extended to computation of force-fields wherein classical ML techniques even though successful have only efficiently modelled small systems.…”