Abstract

We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name. It allows to determine time-dependent external fields for a wide range of quantum control problems, including state-to-state transfer, quantum gate implementation and optimization towards an arbitrary perfect entangler. Krotov's method compares to other gradient-based optimization methods such as gradient-ascent and guarantees monotonic convergence for approximately time-continuous control fields. The user-friendly interface allows for combination with other Python packages, and thus high-level customization.

Highlights

  • We present a new open-source Python package, krotov, implementing the quantum optimal control method of that name

  • By providing a comprehensive set of examples, we enable users of our package to explore the formulation of typical control problems, and to understand how Krotov’s method can solve them

  • The quantum control methods build on a rich field of classical control theory [41, 42]

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Summary

Introduction

Quantum information science has changed our perception of quantum physics from passive understanding to a source of technological advances [1]. By providing a comprehensive set of examples, we enable users of our package to explore the formulation of typical control problems, and to understand how Krotov’s method can solve them. These examples are inspired by recent publications [28,29,30,31,32,33], and show the use of the method in the purview of current research. For hard optimization problems that require several thousand iterations to converge, the Python implementation provided by the krotov package may not be sufficiently fast. Appendices C and D contain installation instructions for the krotov package and link to its online documentation

The quantum control problem
Optimization functional
Iterative control update
Example: state-to-state transition in a two-level system
Common optimization tasks
Complex-valued controls
Optimization towards a quantum gate
Ensemble optimization as a way to ensure robust controls
Optimization of non-linear problems or non-convex functionals
Comparison of Krotov’s method and other optimization methods
Iterative schemes from variational calculus
Krotov’s method
Gradient-free optimization
Choosing an optimization method
First order update
Second order update
Time discretization
Findings
Notes:
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