Speaker
Description
Probing ground-state properties is central to understanding quantum matter, yet conventional approaches usually require many independently prepared copies. This becomes prohibitive when ground-state preparation is costly and only a limited number of copies are available. Here we introduce a coherent readout protocol that processes given $P$ ground-state copies in parallel using controlled evolution under the system Hamiltonian and returns them nearly unchanged; the protocol simultaneously estimates $M$ possibly noncommuting observables to additive error $\varepsilon$, without requiring a coherent ground-state preparation circuit or its inverse. Its worst-case elapsed Hamiltonian evolution time is $\tilde{\mathcal{O}}({\Delta}^{-1} (\varepsilon^{-1}{\sqrt M}/P+1))$, where $\Delta$ is the spectral gap; structured observable sets further improve the $M$ dependence. We establish lower bounds of elapsed evolution time for arbitrary parallel protocols, even when the input copies may be consumed, proving simultaneous optimality in $M,\varepsilon,P$ and $\Delta$ up to logarithmic factors. Among its applications, the protocol performs full tomography of a $d$-dimensional ground state within trace-distance error $\eta$ using $\tilde{\mathcal{O}}(\Delta^{-1}(\eta^{-1}{d}/{P}+1))$ elapsed evolution time, with a nearly matching lower bound. These results establish the fundamental dynamical cost of learning ground states when state copies are scarce.