Adiabatic quantum computation and quantum phase transitions

Details Adiabatic quantum computation and quantum phase transitions Adiabatic quantum computation and quantum phase transitions

2003-08-07

arxiv.org/abs/quant-ph/0308042v2

Physical Review A 69, 062302 (2004)

Physics

Quantum Physics

5 pages, 4 figures, accepted for publication in PRA

Scientific paper

10.1103/PhysRevA.69.062302

We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant.

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