Direct fidelity estimation of generic quantum states

Verifying that quantum protocols prepare states as intended is crucial to modern quantum information science. To this end, a variety of protocols that estimate the fidelity between an ideal pure state and a noisy preparation of the ideal state have been proposed. Direct Fidelity Estimation (DFE) with Pauli measurements is a leading approach in this area that handles arbitrary ideal states using a number of state copies that scales linearly with system dimension, which is vastly preferable to the scaling of full state tomography. Another prominent approach is to employ classical shadows to estimate fidelity using a number of state copies independent of system dimension, albeit with the implicit assumption that the target state has a classical description. In this presentation, we introduce a fidelity estimation protocol for completely arbitrary ideal states using a number of iterations that scales only as the square root of system dimension and discuss its implications. Our protocol uses the quantum amplitude estimation algorithm as a crucial ingredient together with components of classical shadow tomography to produce this speedup over Pauli DFE.