Analytically solvable driven time-dependent two-level quantum systems

TL;DR

This paper introduces a simple algorithm that generates an unlimited number of exact analytical solutions for driven two-level quantum systems, significantly aiding quantum control and computation.

Contribution

The authors present a novel method that determines solutions via a single real function, expanding the set of known analytical solutions for time-dependent two-level systems.

Findings

Generated numerous new exact solutions to the Schrödinger equation.

Demonstrated the method's relevance to qubit control in quantum computing.

Provided a general framework for solving driven two-level systems analytically.

Abstract

Analytical solutions to the time-dependent Schrodinger equation describing a driven two-level system are invaluable to many areas of physics, but they are also extremely rare. Here, we present a simple algorithm that generates an unlimited number of exact analytical solutions. We show that a general single-axis driving term and its corresponding evolution operator are determined by a single real function which is constrained only by a certain inequality and initial conditions. Any function satisfying these constraints yields an exact analytical solution. We demonstrate this method by presenting several new exact solutions to the time-dependent Schrodinger equation. Our general method and many of the new solutions we present are particularly relevant to qubit control in quantum computing applications.