Frank Schäfer - Differentiable Programming for Quantum Control with SciML

Differentiable Programming for Quantum Control with SciML

Frank Schäfer, Universität Basel, Switzerland

Abstract:
Conceptually, it is straightforward to determine the time evolution of a single quantum bit (qubit) for a fixed initial state given its (time-dependent) Hamiltonian or Lindbladian. Depending on the physical context, the dynamics is described by an ordinary or stochastic differential equation. In quantum state control, which is of paramount importance for quantum computation, we aim at solving the inverse problem. That is, starting from a distribution of initial states, we seek protocols that allow us to reach a desired target state by optimization of free parameters of the differential equation (control fields) in a certain time interval. To solve this control problem for a qubit, we implement its dynamics as part of a fully differentiable program. Specifically, we employ a neural network that maps an observation of the state of the qubit to a control field defined via the differential equation for each time interval. The parameters of the neural network are optimized in a series of epochs. Such a procedure should ultimately combine powerful tools from machine learning and scientific computation. Thus, the highly performant ecosystem of SciML with a unified user interface represents an ideal platform for our numerical experiments. We demonstrate the flexibility of SciML and verify the robustness of our method against noise.

Contents
00:00 Welcome!
00:33 Overview: Controlling quantum dynamics with SciML
01:07 Example 1: Quantum optimal control in a closed system
04:04 Example 1: The ODE-based learning scheme
07:36 Example 1: The ODE-based learning process
09:10 Example 2: Quantum optimal control in an open system
11:10 Example 2: The SDE-based learning scheme
11:35 Example 2: The SDE-based learning process
13:41 Future developments: Combination with parameter estimation from experimental data
14:44 Aknowlegements and References

[henry-db]

I didn't know you could do quantum computing with Julia