Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines.

Area of Science:

• Computational Physics
• Quantum Many-Body Systems
• Machine Learning

Background:

• Projective quantum Monte Carlo (PQMC) algorithms are powerful for simulating quantum systems.
• PQMC efficiency relies on accurate trial wave functions, typically found via separate variational minimization.

Purpose of the Study:

• To develop an adaptive wave function for PQMC simulations.
• To integrate unsupervised machine learning for optimizing the wave function during the PQMC simulation.

Main Methods:

• Utilized a restricted Boltzmann machine for an adaptive trial wave function.
• Optimized the wave function in-situ via unsupervised machine learning during PQMC.
• Minimized Kullback-Leibler divergence for wave function ansatz.

Main Results:

• Demonstrated high accuracy for the ferromagnetic quantum Ising chain.
• Achieved precise agreement with Jordan-Wigner theory and loop quantum Monte Carlo simulations.
• Showcased the effectiveness of self-learning PQMC in a sign-problem-free model.

Conclusions:

• The self-learning PQMC technique with adaptive wave functions improves simulation efficiency and accuracy.
• This method eliminates the need for separate variational optimization steps.
• Provides a novel approach for accurate ground-state determination in quantum many-body systems.