More Tools for Quantum Control

Domenico D'Alessandro

In this chapter, we discuss some more tools for the control of quantum systems. Some of these are commonly considered in the physics and chemistry literature. Some others, like the Lyapunov control method, have been very well studied in the control literature and have then been extended to quantum systems.

A. I. Solomon, Sonia G. Schirmer

Koen J. Mesman, Francesco Battistel, Edgar Reehuis +5 more

Scaling up the number of qubits and accelerating quantum algorithms are important steps towards reaching quantum advantage. This poses heavy demands, as pulses need to be distributed to an increasing number of control channels and variational algorithms require rapid interleaving of quantum and classical computation. Assessing the bottlenecks in the control stack is therefore key to prepare it for reaching quantum advantage. However, existing benchmark suites suffer from indirect access to control hardware, limiting accuracy. In this work, we present Q-Profile, a tool to profile quantum control stacks using a direct connection from the host CPU to the control stack, providing fine accuracy in measuring runtime and allowing to identify performance bottlenecks. We demonstrate our tool by benchmarking the Quantum Approximate Optimization Algorithm on a Qblox Cluster for a virtual 4 to 14-qubit transmon system and identify the major execution bottlenecks. We estimate a 1.40x total runtime speedup by using an active qubit reset, and demonstrate a further 1.37x speedup by parallel control module initialization. The presented method of profiling is included in the open-source Quantify quantum control software, making it applicable to other control-stack providers and to other benchmarks, while still providing detailed information. By extension, this tool will enable identifying and eliminating bottlenecks for future quantum acceleration.

Prateek Tandon, Stanley Lam, Ben Shih +3 more

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Ugo Boscain, Mario Sigalotti, Dominique Sugny

Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This review aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This review describes modern aspects of optimal control theory, with a particular focus on the Pontryagin Maximum Principle, which is the main tool for determining open-loop control laws without experimental feedback. The different steps to solve an optimal control problem are discussed, before moving on to more advanced topics such as the existence of optimal solutions or the definition of the different types of extremals, namely normal, abnormal, and singular. The review covers various quantum control issues and describes their mathematical formulation suitable for optimal control. The optimal solution of different low-dimensional quantum systems is presented in detail, illustrating how the mathematical tools are applied in a practical way.