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In measurement-based quantum computation, quantum algorithms are implementedvia sequences of measurements. We describe a translationally invariantfinite-range interaction on a one-dimensional qudit chain and prove that asingle-shot measurement of the energy of an appropriate computational basisstate with respect to this Hamiltonian provides the output of any quantumcircuit. The required measurement accuracy scales inverse polynomially with thesize of the simulated quantum circuit. This shows that the implementation ofenergy measurements on generic qudit chains is as hard as the realization ofquantum computation. Here a ''measurement'' is any procedure that samples fromthe spectral measure induced by the observable and the state underconsideration. As opposed to measurement-based quantum computation, thepost-measurement state is irrelevant.

A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation