Speakers
Description
Coherent inverse access is needed in amplitude amplification, time-reversal tests, and scrambling probes, but exact black-box inversion of an unknown $d$-dimensional unitary has quadratic query cost. We ask what changes when the oracle is a Hamiltonian evolution $U(x)=\exp(i\sum_j x_j H_j)$ with known generators and unknown couplings. In a compiled-structure query model, fixed gates may depend on the known generator algebra while only coherent calls to the unknown forward evolution are counted. For one Hamiltonian with known eigenspaces, $K-1$ queries suffice for $K$ distinct eigenvalues, and the optimum is an additive sumset condition on the distinct spectrum. For multi-parameter families, Wedderburn reduction removes passive multiplicity wires, and local active-block inverses can be recombined by synchronizing their query lengths and residual scalar phases. Determinant, trace-vector, and automatic-completion constructions give explicit exact protocols. Exchange, hopping, and collective-spin examples show query budgets controlled by active representation data rather than by the full many-body Hilbert space.
| Topic | Theoretical foundations of quantum learning |
|---|