  We introduce an approximate description of an $N$-qubit state, which contains
sufficient information to estimate the expectation value of any observable with
precision independent of $N$. We show, in fact, that the error in the
estimation of the observables' expectation values decreases as the inverse of
the square root of the number of the system's identical preparations and
increases, at most, linearly in a suitably defined, $N$-independent, seminorm
of the observables. Building the approximate description of the $N$-qubit state
only requires repetitions of single-qubit rotations followed by single-qubit
measurements and can be considered for implementation on today's Noisy
Intermediate-Scale Quantum (NISQ) computers. The access to the expectation
values of all observables for a given state leads to an efficient variational
method for the determination of the minimum eigenvalue of an observable. The
method represents one example of the practical significance of the approximate
description of the $N$-qubit state. We conclude by briefly discussing
extensions to generative modelling and with fermionic operators.
