Training Schrödinger’s cat: quantum optimal control

Abstract

Abstract. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments. ForewordThe authors of this paper represent the QUAINT consortium, a European Coordination Action on Optimal Control of Quantum Systems, funded by the European Commission Framework Programme 7, Future Emerging Technologies FET-OPEN programme and the Virtual Facility for Quantum Control (VF-QC). This consortium has considerable expertise in optimal control theory and its applications to quantum systems, both in existing areas, such as spectroscopy and imaging, and in emerging quantum technologies, such as quantum information processing, quantum communication, quantum simulation a e-mail: fwm@lusi.uni-sb.de and quantum sensing. The list of challenges for quantum control has been gathered by a broad poll of leading researchers across the communities of general and mathematical control theory, atomic, molecular-, and chemical physics, electron and nuclear magnetic resonance spectroscopy, as well as medical imaging, quantum information, communication and simulation. 144 experts in these fields have provided feedback and specific input on the state of the art, mid-term and long-term goals. Those have been summarized in this document, which can be viewed as a perspectives paper, providing a roadmap for the future development of quantum control. Because such an endeavour can hardly ever be complete (there are many additional areas of quantum control applications, such as spintronics, nano-optomechanical technologies etc.), this roadmap

Controlling open quantum systems: tools, achievements, and limitations

“…Obviously, controllability analysis based on the Lie rank condition for the Hamiltonian alone cannot provide any information on time evolutions which change the purity of the system's state, P = Tr ρ 2 S (t) . By and large, controllability of open quantum systems still remains uncharted territory to date [1]. This refers in particular to dynamic controllability where the analysis accounts for available dynamical resources such as coupling to external fields and environmental degrees of freedom, or measurements, in contrast to kinematic controllability.…”

Fully efficient time-parallelized quantum optimal control algorithm

“…Optimal control was used in physical chemistry in order to steer chemical reactions [3], but also for spin systems [10,11] with applications in Nuclear Magnetic Resonance [7,[12][13][14][15][16] and Magnetic Resonance Imaging [17][18][19]. Recently, optimal control has attracted attention in view of applications to quantum information processing, for example as a tool to implement high-fidelity quantum gates in minimum time [4,20,21]. Generally, algorithms can also be designed to account for experimental imperfections or constraints related to a specific material or device [4].…”

Symmetry criteria for quantum simulability of effective interactions

“…However, the approach of the pioneering age of decomposing every target gate into a sequence of cnot and local gates is, in practice, all too often imprecise or slow. So implementing gates or simulating Hamiltonians with high fidelity rather asks for optimal control techniques, as explained in a recent roadmap [42]. As a precondition, here we step back to the Hamiltonian level and give criteria for simulability and controllability.…”