Enhancing Quantum Algorithms Through Integration with Model Predictive Control Concepts

There is currently significant interest in developing new algorithms and applications for quantum computers. Hybrid quantum-classical algorithms based on parameterized quantum circuits, including variational and feedback-based quantum algorithms, have been developed for applications ranging from combinatorial optimization to quantum simulation. These classes of hybrid quantum-classical algorithms have ties to quantum optimal control and quantum Lyapunov control, respectively. We present a new type of hybrid quantum-classical algorithm inspired by concepts from model predictive control (MPC). We relate parameterized quantum circuits to quantum control systems, assigning values to quantum circuit parameters in a manner that is analogous to setting the values of control variables in MPC, which uses a combination of feedback and model-based, moving-horizon optimization to achieve a desired control objective. We discuss the benefits and limitations of the MPC-based approach compared with a Lyapunov-based approach and investigate how the selection of design parameters such as prediction horizon length and sampling time impact the algorithm.