Source-linked AI summary
Quantum Adiabatic Brachistochrone
A. T. Rezakhani, W. -J. Kuo, A. Hamma, D. A. Lidar, P. Zanardi
TL;DR
The paper formulates AQC as a time-minimization problem over control paths and recasts the optimal paths as geodesics of a natural Riemannian metric. Its examples show improved performance from higher-dimensional controls and connect that performance with curvature and entanglement.
Problem
AQC needs a way to choose control paths that minimize runtime while respecting a local adiabatic condition.
Source: p. 2Method
The quantum adiabatic brachistochrone (QAB) minimizes a time functional over control paths and gives the resulting paths a Riemannian-geometric description.
Source: pp. 1–2Results
In Grover search, the 2-d optimal path usually has lower error than the RC path, and the 4-d path further improves the comparison shown.
Source: p. 3Takeaways & Limitations
The examples show that increasing control-space dimension can improve adiabatic-algorithm performance, while entanglement and curvature help characterize the paths.
Source: p. 4The method requires an exact gap or an estimate, and finding the exact gap can be as hard as solving the problem itself.
Source: p. 2
Abstract
from arXiv · showhide
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.