Direct Fidelity Estimation for Generic Quantum States

Verifying the proper preparation of quantum states is essential in modern quantum information science. Various protocols have been developed to estimate the fidelity of quantum states produced by different parties. Direct fidelity estimation is a leading approach, as it typically requires a number of measurements that scale linearly with the Hilbert space dimension, making it far more efficient than full state tomography. In this article, we introduce a novel fidelity estimation protocol for generic quantum states, with an overall computational cost that scales only as the square root of the Hilbert space dimension. Furthermore, our protocol significantly reduces the number of required measurements and the communication cost between parties to finite. This protocol leverages the quantum amplitude estimation algorithm in conjunction with classical shadow tomography to achieve these improvements.