QuantumControl.jl

QuantumControl.jl is a Julia framework for quantum dynamics and control.

Quantum optimal control [1–8] attempts to steer a quantum system in some desired way by finding optimal control parameters or control fields inside the system Hamiltonian or Liouvillian. Typical control tasks are the preparation of a specific quantum state or the realization of a logical gate in a quantum computer ("pulse level control"). Thus, quantum control theory is a critical part of realizing quantum technologies at the lowest level. Numerical methods of open-loop quantum control (methods that do not involve measurement feedback from a physical quantum device) such as Krotov's method [9–14] and GRAPE [15, 16] address the control problem by simulating the dynamics of the system and then iteratively improving the value of a functional that encodes the desired outcome.

Functional

Mathematically, the control problem is the minimization of a functional of the form

\[J(\{ϵ_l(t)\}) = J_T(\{|Ψ_k(T)⟩\}) + λ_a \, \underbrace{∑_l \int_{0}^{T} g_a(ϵ_l(t)) \, dt}_{=J_a(\{ϵ_l(t)\})} + λ_b \, \underbrace{∑_k \int_{0}^{T} g_b(|Ψ_k(t)⟩) \, dt}_{=J_b(\{|Ψ_k(t)⟩\})}\,,\]

where $\{ϵ_l(t)\}$ is a set of control functions defined between the initial time $t=0$ and the final time $t=T$, and $\{|Ψ_k(t)⟩\}$ is a set of "trajectories" evolving from a set of initial states $\{|\Psi_k(t=0)⟩\}$ under the controls $\{ϵ_l(t)\}$. The full functional consists of the final-time functional $J_T$, a control-dependent running cost $J_a$ weighted by $λ_a$, and sometimes a state-dependent running cost $J_b$ weighted by $λ_b$. The states can be Hilbert space vectors or density matrices, and the equation of motion is implicit, typically the Schrödinger or Liouville equation.

The QuantumControl.jl package provides a single coherent API for solving the quantum control problem with the packages in the JuliaQuantumControl organization. Different optimization methods target specific variants of the above functional.

Getting Started

• See the installation instructions on Github.

• Look at a simple example for a state-to-state transition with GRAPE to get a feeling for how the QuantumControl package is intended to be used, or look at the larger list of Examples.

• Read the Glossary and Overview to understand the philosophy of the framework.

Contents

• Glossary
• Overview
• • Setting up control problems
  • Controls and control parameters
  • Time propagation
  • Optimization
• Control Methods
• • Krotov's Method
  • GRAPE
• Howto

Examples

• Examples
• • Krotov-specific examples
  • GRAPE-specific examples

API

• QuantumControl Public API

Sub-Packages

• QuantumPropagators Package

History

See the Releases on Github.