



01484nas a2200121   4500008004100000245004900041210004600090260001500136520114100151100001701292700001601309856003701325       2019                        eng d00aAn approximate description of quantum states0 aapproximate description of quantum states  c2019/11/133 a<p>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&#39; expectation values decreases as the inverse of the square root of the number of the system&#39;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&#39;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</p>1 aPaini, Marco1 aKalev, Amir  uhttps://arxiv.org/abs/1910.10543