An approximate description of quantum states
Abstract
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 singlequbit rotations followed by singlequbit measurements and can be considered for implementation on today's Noisy IntermediateScale 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.10543
 Bibcode:
 2019arXiv191010543P
 Keywords:

 Quantum Physics
 EPrint:
 9 pages + 7 pages