Efficient sample-optimal learning in a fixed Fock basis

Determine whether states sparse in a fixed, possibly unknown, Fock basis can be learned with sample-optimal and time-efficient algorithms.

Background

The paper relates computational-basis sparsity to physically motivated sparse representations in bosonic and fermionic systems. Existing work is described as providing either optimal sample complexity without a known efficient implementation or sample- and time-efficient algorithms without sample optimality. The unresolved problem is to achieve both properties for states sparse in a fixed Fock basis.