Optimal control and machine learning of quantum device dynamics

In this work, we first consider standard quantum control problems for superconducting transmon qubits. Such quantum systems have been studied extensively both from an analytical and a numerical perspective MSG TMW16. Analytical pulses usually show dependencies from system parameters that are not easily found in numerical solutions. Therefore, our approach is then to employ neural networks to learn the functional dependence of optimal quantum control solutions from system parameters. We show that we can optimize such solutions analytically for single and two-qubit gates using either very few parameter samples or large numbers of pulse frequencies for large parameter ranges. Afterward, we move to a higher level of optimization. We consider variational gates in trapped-ion quantum computers MMN SEL&al22. We show that our reinforcement learning algorithm assisted by a continuous optimizer can construct effective solutions to the gate synthesis problem that matches and surpasses standard circuit compilers. Next, we consider variational optimization of non-linear maps HCS&al23 acting on quantum states such as entanglement purification protocols. An entanglement purification protocol acts as a highly non-linear map, but it still outputs a faithful representation of a quantum system. Optimizing it for a specific family of states requires reducing the number of operations needed to retrieve the original state. This optimization has the potential to make purification protocols easier to implement on a quantum device. In fact, the exponential scaling of the purification protocol with the number of states DB07 implies that such protocols may not be applied directly without careful engineering. We also show that the performance of standard purification protocols for arbitrary two-qubit input states leads to poor output values of the concurrence. Our optimized protocols prove instead able to increase the value of the concurrence above the maximum limit of traditional analytical protocols. We also show how the twirling operation becomes an obstacle to the performance of the protocol itself when considering random two-qubit states, although it is a useful tool in the design of entanglement purification protocols. Finally, we study parameter sampling in quantum circuits, focusing in particular on the LCU methods. Such problems are particularly interesting for meta-variational settings CKA21 where we compute the average over observables evaluated at different points in the parameter space. They are also relevant for optimal quantum control algorithms because the computation of the fidelity with respect to a target operation is the basis of most optimal quantum control routines. In conclusion, we analyze several optimization problems that are relevant for quantum science and technology. We show that machine learning-assisted solutions can be applied successfully to engineer optimal quantum control pulses and compilation strategies based on variational angles. Also in the context of entanglement purification, we show how our optimized protocols can surpass current strategies for multiparametric families of states.