Geometrizing quantum adiabatic computation - Ali Rezakhani

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 is demonstrated through some examples, where I show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.