Improved Quantum Algorithms for Fidelity Estimation

Understand

Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view.

• Yet, in general, it is difficult to give good estimates of fidelity, especially when one works with mixed states over Hilbert spaces of very high dimension.
• Although, there has been some progress on fidelity estimation, all prior work either requires a large number of identical copies of the relevant states, or relies on unproven heuristics.
• In this work, we improve on both of these aspects by developing new and efficient quantum algorithms for fidelity estimation with provable performance guarantees in case at least one of the states is approximately low-rank.