  A method to study strongly interacting quantum many-body systems at and away
from criticality is proposed. The method is based on a MERA-like tensor network
that can be efficiently and reliably contracted on a noisy quantum computer
using a number of qubits that is much smaller than the system size. We prove
that the outcome of the contraction is stable to noise and that the estimated
energy upper bounds the ground state energy. The stability, which we
numerically substantiate, follows from the positivity of operator scaling
dimensions under renormalization group flow. The variational upper bound
follows from a particular assignment of physical qubits to different locations
of the tensor network plus the assumption that the noise model is local. We
postulate a scaling law for how well the tensor network can approximate ground
states of lattice regulated conformal field theories in d spatial dimensions
and provide evidence for the postulate. Under this postulate, a
$O(\log^{d}(1/\delta))$-qubit quantum computer can prepare a valid
quantum-mechanical state with energy density $\delta$ above the ground state.
In the presence of noise, $\delta = O(\epsilon \log^{d+1}(1/\epsilon))$ can be
achieved, where $\epsilon$ is the noise strength.
