Quantum simulators, continuous-time automata, and translationally invariant systems.
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems in 1D. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest-neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.
Vollbrecht
K G H
KG
Max-Planck Institut für Quantenoptik, Hans-Kopfermann-Str. 1, Garching, D-85748, Germany.
Cirac
J I
JI