Improve Virational Quantum Eigensolver by Many-Body Localization

Variational quantum algorithms have been widely demonstrated in both experimental and theoretical contexts to have extensive applications in quantum simulation, optimization, and machine learning. However, the exponential growth in the dimension of the Hilbert space results in the phenomenon of vanishing parameter gradients in the circuit as the number of qubits and circuit depth increase, known as the barren plateau phenomena. In recent years, research in non-equilibrium statistical physics has led to the discovery of the realization of many-body localization. As a type of floquet system, many-body localized floquet system has phase avoiding thermalization with an extensive parameter space coverage and have been experimentally demonstrated can produce time crystals. We applied this circuit to the variational quantum algorithms for the calculation of many-body ground states and studied the variance of gradient for parameter updates under this circuit. We found that this circuit structure can effectively avoid barren plateaus. We also analyzed the entropy growth, information scrambling, and optimizer dynamics of this circuit. Leveraging this characteristic, we designed a new type of variational ansatz, called the 'many-body localization ansatz'. We applied it to solve quantum many-body ground states and examined its circuit properties. Our numerical results show that our ansatz significantly improved the variational quantum algorithm.