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

The critical point and the critical exponents for a quantum phase transition can be determined using the finite-size scaling (FSS) analysis.  However, this method is computationally expensive for many-body systems in which the size of the Hilbert space grows exponentially with the size of the system. In recent years, digital quantum simulators (DQS) have emerged as a promising platform to carry out classically intractable calculations for quantum many-body systems. An important question that arises is whether the FSS method has an efficient implementation on a DQS. In this work, we take a step towards addressing this question. We perform a proof-of-principle demonstration of FSS for the phase transition in Quantum Rabi Model using the Quantum Restricted Boltzmann Machine algorithm. Using the quantum algorithm, we work out the critical coupling strength beyond which the system enters a super-radiant phase. Our work opens up a new direction in the study of Phase Transitions on DQS.