  We describe a resource-efficient approach to studying many-body quantum
states on noisy, intermediate-scale quantum devices. We employ a sequential
generation model that allows us to bound the range of correlations in the
resulting many-body quantum states. From this, we characterize situations where
the estimation of local observables does not require the preparation of the
entire state. Instead smaller patches of the state can be generated from which
the observables can be estimated. This can potentially reduce circuit size and
number of qubits for the computation of physical properties of the states.
Moreover, we show that the effect of noise decreases along the computation. Our
results apply to a broad class of widely studied tensor network states and can
be directly applied to near-term implementations of variational quantum
algorithms.
