A long standing challenge in the foundations of quantum mechanics is the verification of alternative collapse theories despite their mathematical similarity to decoherence. To this end, we suggest a novel method based on dynamical decoupling. Experimental observation of non-zero saturation of the decoupling error in the limit of fast decoupling operations can provide evidence for alternative quantum theories. The low decay rates predicted by collapse models are challenging, but high fidelity measurements as well as recent advances in decoupling schemes for qubits let us explore a similar parameter regime to experiments based on macroscopic superpositions. As part of the analysis we prove that unbounded Hamiltonians can be perfectly decoupled. We demonstrate this on a novel dilation of a Lindbladian to a fully Hamiltonian model that induces exponential decay.

The last decade has witnessed remarkable progress in the development of quantum technologies. Although fault-tolerant devices likely remain years away, the noisy intermediate-scale quantum devices of today may be leveraged for other purposes. Leading candidates are variational quantum algorithms (VQAs), which have been developed for applications including chemistry, optimization, and machine learning, but whose implementations on quantum devices have yet to demonstrate improvements over classical capabilities. In this Perspective, we propose a variety of ways that progress toward this potential crossover point could be informed by quantum optimal control theory. To set the stage, we identify VQAs and quantum optimal control as formulations of variational optimization at the circuit level and pulse level, respectively, where these represent just two levels in a broader hierarchy of abstractions that we consider. In this unified picture, we suggest several ways that the different levels of abstraction may be connected, in order to facilitate the application of quantum optimal control theory to VQA challenges associated with ansatz selection, optimization landscapes, noise, and robustness. A major theme throughout is the need for sufficient control resources in VQA implementations; we discuss different ways this need can manifest, outline a variety of open questions, and conclude with a look to the future.

In this work we derive a lower bound for the minimum time required to implement a target unitary transformation through a classical time-dependent field in a closed quantum system. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest permitted control field amplitude. These findings reveal some properties of the reachable set of operations, explicitly analyzed for a single qubit. Moreover, for fully controllable systems, we identify a lower bound for the time at which all unitary gates become reachable. We use numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe the relationship between the highest control field amplitude and the minimum evolution time remarkably well. Finally, we discuss both challenges and ways forward for obtaining tighter bounds for higher dimensional systems, offering a discussion about the mathematical form and the physical meaning of the bound.

We study the controllability of a central spin guided by a classical field and interacting with a spin bath and show that the central spin is fully controllable independently of the number of bath spins. Additionally we find that for unequal system-bath couplings even the bath becomes controllable by acting on the central spin alone. We then analyze numerically how the time to implement gates on the central spin scales with the number of bath spins and conjecture that for equal system-bath couplings it reaches a saturation value. We provide evidence that sometimes noise can be effectively suppressed through control.

A method for generating entangled cat states of two modes of a microwave cavity field is proposed. Entanglement results from the interaction of the field with a beam of atoms crossing the microwave resonator, giving rise to non-unitary dynamics of which the target entangled state is a fixed point. We analyse the robustness of the generated two-mode photonic "cat state" against dephasing and losses by means of numerical simulation. This proposal is an instance of quantum reservoir engineering of photonic systems.