Heidelberg 2007 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 4: Quantenmechanik, Symmetrien, Integrable Systeme und Quanteninformationstheorie
MP 4.3: Talk
Tuesday, March 6, 2007, 18:00–18:30, KIP SR 1.403
Adiabatic quantum algorithms as quantum phase transitions: 1st versus 2nd order — •Ralf Schuetzhold and Gernot Schaller — Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to those of first order. With this insight, we propose a novel adiabatic quantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact cover), which is significantly faster than previous proposals according to numerical simulations (up to 20 qubits). These findings suggest that adiabatic quantum algorithms can solve NP-complete problems such as 3-SAT much faster than the Grover search routine (yielding a quadratic enhancement), possibly even with an exponential speed-up.