The Power of Quantum Systems on a Line

: We study the computational strength of quantum particles (each of finite dimensionality) arranged on a line. First, we prove that it is possible to perform universal adiabatic quantum computation using a one-dimensional quantum system (with 9 states per particle). This might have practical implications for experimentalists interested in constructing an adiabatic quantum computer. Building on the same construction, but with some additional technical effort and 12 states per particle, we show that the problem of approximating the ground state energy of a system composed of a line of quantum particles is QMA-complete; QMA is a quantum analogue of NP. This is in striking contrast to the fact that the analogous classical problem, namely, one-dimensional MAX-2-SAT with nearest neighbor constraints, is in P. The proof of the QMA-completeness result requires an additional idea beyond the usual techniques in the area: Not all illegal configurations can be ruled out by local checks, so inste...

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Dorit Aharonov, Daniel Gottesman, Sandy Irani, Julia Kempe
• Keywords: Adiabatic Quantum, FOCS 2007, Quantum, Quantum Particles, Theoretical Computer Science