Quantum Adiabatic Brachistochrone

Abstract

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A 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 two examples, where we 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.

4 pages, 2 figures

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• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Accuracy vs run time in adiabatic quantum search
• Optimal control for unitary preparation of many-body states: application to Luttinger liquids
• Feedback-controlled adiabatic quantum computation
• Avoid First Order Quantum Phase Transition by Changing Problem Hamiltonians