QuantumCollocation.jl

QuantumCollocation.jl sets up and solves quantum control problems as nonlinear programs (NLPs). In this context, a generic quantum control problem looks like

\[\begin{aligned} \arg \min_{\mathbf{Z}}\quad & J(\mathbf{Z}) \\ \nonumber \text{s.t.}\qquad & \mathbf{f}(\mathbf{Z}) = 0 \\ \nonumber & \mathbf{g}(\mathbf{Z}) \le 0 \end{aligned}\]

where $\mathbf{Z}$ is a trajectory containing states and controls, from NamedTrajectories.jl.

We provide a number of problem templates for making it simple and easy to set up and solve certain types of quantum optimal control problems. These templates all construct a DirectTrajOptProblem object from DirectTrajOpt.jl, which stores all the parts of the optimal control problem.

Get started

The problem templates are broken down by the state variable of the problem being solved.

Ket Problem Templates:

• Quantum State Smooth Pulse Problem
• Quantum State Minimum Time Problem
• Quantum State Sampling Problem

Unitary Problem Templates:

• Unitary Smooth Pulse Problem
• Unitary Minimum Time Problem
• Unitary Sampling Problem

Background

Problem Templates are reusable design patterns for setting up and solving common quantum control problems.

For example, a UnitarySmoothPulseProblem is tasked with generating a pulse sequence $a_{1:T-1}$ in orderd to minimize infidelity, subject to constraints from the Schroedinger equation,

\[ \begin{aligned} \arg \min_{\mathbf{Z}}\quad & |1 - \mathcal{F}(U_T, U_\text{goal})| \\ \nonumber \text{s.t.} \qquad & U_{t+1} = \exp\{- i H(a_t) \Delta t_t \} U_t, \quad \forall\, t \\ \end{aligned}\]

while a UnitaryMinimumTimeProblem minimizes time and constrains fidelity,

\[ \begin{aligned} \arg \min_{\mathbf{Z}}\quad & \sum_{t=1}^T \Delta t_t \\ \qquad & U_{t+1} = \exp\{- i H(a_t) \Delta t_t \} U_t, \quad \forall\, t \\ \nonumber & \mathcal{F}(U_T, U_\text{goal}) \ge 0.9999 \end{aligned}\]

In each case, the dynamics between knot points$(U_t, a_t)$ and $(U_{t+1}, a_{t+1})$ are enforced as constraints on the states, which are free variables in the solver; this optimization framework is called direct trajectory optimization.

Problem templates give the user the ability to add other constraints and objective functions to this problem and solve it efficiently using Ipopt.jl and MathOptInterface.jl under the hood.