Physics – Quantum Physics
Scientific paper
2007-10-08
Physics
Quantum Physics
19 pages, transition rules for the CA corrected
Scientific paper
10.1088/1367-2630/10/9/093004
In measurement-based quantum computation, quantum algorithms are implemented via sequences of measurements. We describe a translationally invariant finite-range interaction on a one-dimensional qudit chain and prove that a single-shot measurement of the energy of an appropriate computational basis state with respect to this Hamiltonian provides the output of any quantum circuit. The required measurement accuracy scales inverse polynomially with the size of the simulated quantum circuit. This shows that the implementation of energy measurements on generic qudit chains is as hard as the realization of quantum computation. Here a ''measurement'' is any procedure that samples from the spectral measure induced by the observable and the state under consideration. As opposed to measurement-based quantum computation, the post-measurement state is irrelevant.
Janzing Dominik
Wocjan Pawel
Zhang Shengyu
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