Learning beyond polylogarithmic depth

Identify structural conditions under which n-qubit quantum circuits of depth exceeding polylog(n) can be learned efficiently (e.g., in polynomial or quasipolynomial classical time), and develop corresponding learning algorithms with provable guarantees.

Background

The work establishes efficient learning for constant-depth circuits and shows hardness for general log-depth circuits in the non-geometric setting. In geometrically local settings, the authors obtain learning up to polylogarithmic depth (depending on dimension) with polynomial or quasipolynomial time.

The open question targets the boundary between tractable and intractable depths and seeks additional structural assumptions that would enable efficient learning beyond polylogarithmic depth.