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Geometrization of quantum adiabatic computation

Ali Rezakhani, University of Southern California

(Session 8 : Saturday from 4:30-5:00)

Abstract. A time-optimal approach to adiabatic quantum computation (AQC) will be formulated. The corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC and its relation with quantum phase transitions are demonstrated through some examples, where we show that the geometric formulation leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.