Accurate Learning of Equivariant Quantum Systems from a Single Ground State
This improves efficiency for quantum physics applications like molecular dynamics and variational quantum algorithms, though it is incremental as it builds on prior provably efficient algorithms.
The paper tackles the problem of predicting properties across system parameters for quantum systems by learning from a single ground state sample, achieving prediction error that tends to zero in the thermodynamic limit.
Predicting properties across system parameters is an important task in quantum physics, with applications ranging from molecular dynamics to variational quantum algorithms. Recently, provably efficient algorithms to solve this task for ground states within a gapped phase were developed. Here we dramatically improve the efficiency of these algorithms by showing how to learn properties of all ground states for systems with periodic boundary conditions from a single ground state sample. We prove that the prediction error tends to zero in the thermodynamic limit and numerically verify the results.