Session B18: Invited Session: Optimal Control of Quantum Systems

Optimizing control for implementing error correction in superconducting quantum circuits

Fault-tolerant quantum computing hinges on implementing gates and measurement with fidelities above the threshold for error correction schemes. We have constructed a nine qubit device with integrated control and readout to implement the repetition code error correction scheme, a one-dimensional version of the surface code. We show how rapid scans, randomized benchmarking, and the error correction code itself can be used to optimize gates in this complex quantum device to fidelities which allow for protecting states from environmentally-induced bit errors.   

Controlling open quantum systems: Tools, achievements, limitations

Quantum control is an important prerequisite for quantum devices. A major obstacle is the fact that a quantum system can never completely be isolated from its environment. The interaction with the environment causes decoherence. Optimal control theory is a tool that can be used to identify control strategies in the presence of decoherence. I will show how to adapt optimal control theory to quantum information tasks for open quantum systems and present examples for cold atoms and superconducting qubits. In particular, I will discuss how non-Markovianity of the open system time evolution can be exploited for control. The perspective on decoherence only as the adversary of quantum control is nevertheless too narrow. There exist a number of control tasks, such as cooling and measurement, that can only be achieved by an interplay of control and dissipation. I will show how to utilize optimal control theory to derive efficient cooling strategies when the timescales of coherent dynamics and dissipation are very different. Our approach can be generalized to quantum reservoir engineering, opening up new avenues for control.   

Quantum Control Engineering with Trapped Ions

Technologies fundamentally enabled by quantum mechanics are poised to transform a broad range of applications from computation to precision metrology over the coming decades. This talk will introduce a new field of research which is seeing concepts from control engineering translated to the domain of quantum mechanics in an effort to realize the full potential of engineered quantum technologies. We focus on understanding the physics underlying controlled quantum dynamics in the presence of rapidly fluctuating time-dependent Hamiltonians, leveraging the unique capabilities provided by trapped ions as a model quantum system. Our results introduce and experimentally validate generalized filter-transfer functions which cast arbitrary quantum control operations on qubits as noise spectral filters. We demonstrate the utility of these constructs for directly predicting the evolution of a quantum state in a realistic noisy environment, for developing novel robust control and sensing protocols, and for improving the stability of atomic clocks. This work demonstrates how quantum control can be leveraged to overcome some of the most challenging problems in quantum engineering, and even provide totally new functionality to quantum systems.   

A general transfer-function approach to noise filtering in open-loop quantum control

Hamiltonian engineering via unitary open-loop quantum control provides a versatile and experimentally validated framework for manipulating a broad class of non-Markovian open quantum systems of interest, with applications ranging from dynamical decoupling and dynamically corrected quantum gates, to noise spectroscopy and quantum simulation. In this context, transfer-function techniques directly motivated by control engineering have proved invaluable for obtaining a transparent picture of the controlled dynamics in the frequency domain and for quantitatively analyzing performance. In this talk, I will show how to identify a computationally tractable set of ``fundamental filter functions,'' out of which arbitrary filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental set suffices to characterize the error suppression capabilities of the control protocol in both the time and frequency domain. I will show, in particular, how the resulting notion of ``filtering order'' reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the ``cancellation order,'' traditionally defined in the Magnus sense. Implications for current quantum control experiments will be discussed.