Stochastic representation of many-body quantum states

Area of Science:

• Quantum mechanics
• Computational physics
• Machine learning

Background:

• The quantum many-body problem faces a curse of dimensionality, making numerical solutions computationally expensive.
• Deep neural networks excel at handling high-dimensional, correlated functions.

Purpose of the Study:

• To develop a computationally scalable method for solving the quantum many-body problem.
• To leverage machine learning for efficient quantum wavefunction representation and ground state determination.

Main Methods:

• Representing wavefunctions stochastically as sample points.
• Reducing the ground state search to a supervised learning regression task.
• Utilizing (anti)symmetric properties of fermionic/bosonic wavefunctions for data augmentation.

Main Results:

• Demonstrated that ground state search can be framed as a regression problem.
• Showcased data augmentation via wavefunction symmetry properties.
• Achieved more robust and scalable propagation of ansatz towards ground states.

Conclusions:

• Machine learning offers a viable and scalable alternative to traditional methods for the quantum many-body problem.
• Stochastic wavefunction representation simplifies complex quantum computations.