科研之友
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摘要
A decade ago Kitaev%26apos;s toric code model established the new paradigm of topological quantum computation. Due to remarkable theoretical and experimental progress, the quantum simulation of such complex many-body systems is now within the realms of possibility. Here we consider the question, to which extent the ground states of small toric code systems differ from local-unitary (LU)-equivalent graph states. We argue that simplistic (though experimentally attractive) setups obliterate the differences between the toric code and equivalent graph states; hence we search for the smallest setups on the square and triangular lattices, such that the quasilocality of the toric code Hamiltonian becomes a distinctive feature. To this end, a purely geometric procedure to transform a given toric code setup into a local-Clifford (LC)-equivalent graph state is derived. In combination with an algorithmic computation of LC-equivalent graph states, we find the smallest nontrivial setup on the square lattice to contain five plaquettes and 16 qubits; on the triangular lattice the number of plaquettes and qubits is reduced to four and nine, respectively.
- 出版日期2012-8-28
