Energy Optimal Interpolation in Quantum Evolution

TL;DR

This paper develops a framework for determining the energy optimal Hamiltonian in quantum evolution, using variational and geometric methods, and connects it to the quantum brachistochrone problem.

Contribution

It introduces a general interpolation framework for quantum evolution and demonstrates its application to energy optimization, including the quantum brachistochrone as a special case.

Findings

Established a variational approach for energy optimal quantum evolution.

Connected the interpolation framework to the quantum brachistochrone problem.

Provided analysis of special cases within the framework.

Abstract

We introduce the concept of interpolation in quantum evolution and present a general framework to find the energy optimal Hamiltonian for a quantum system evolving among a given set of middle states using variational and geometric methods. A few special cases are carefully studied. The quantum brachistochrone problem is proved as a special case.