  As quantum technologies mature, the development of tools for benchmarking
their ability to prepare and manipulate complex quantum states becomes
increasingly necessary. A key concept, the state overlap between two quantum
states, offers a natural tool to verify and cross-validate quantum simulators
and quantum computers. Recent progress in controlling and measuring large
quantum systems has motivated the development of state overlap estimators of
varying efficiency and experimental complexity. Here, we demonstrate a
practical approach for measuring the overlap between quantum states based on a
factorable quasiprobabilistic representation of the states, and compare it with
methods based on randomised measurements. Assuming realistic noisy intermediate
scale quantum (NISQ) devices limitations, our quasiprobabilistic method
outperforms the best circuits designed for state-overlap estimation for n-qubit
states, with n > 2. For n < 7, our technique outperforms also the currently
best direct estimator based on randomised local measurements, thus establishing
a niche of optimality.
