The Work Program is divided into 6 interconnected scientific Work Packages, and the seventh Work Package is for management and dissemination (see the Work Package Table below).
WP1 is devoted to the development of advanced methods for quantum control – highly accurate control of quantum systems by suitably designed external fields – which is the key enabling force in all quantum technologies. These new, more efficient methods for quantum control will be developed and used in the following work packages WP2-WP6. These include adiabatic and composite quantum control in which the Vitanov group has long traditions at the highest international level. They are supplemented by the red-hot approach of quantum control designed by machine learning methods. All these methods will be applied to qubits, and their application to qudits (quantum systems with d states) will be also explored. A special and very important tool for quantum control is dynamical decoupling, which decouples the quantum system from external noise and thereby extends its coherence time – a crucial factor in all quantum technologies.
WP2 is devoted to the design of new highly accurate elements for quantum computing. These include high-fidelity single-qubit and two-qubit quantum gates, specially designed for superconducting and trapped-ion qubits – the two leading quantum computing platforms. These gates will be used to construct optimized quantum circuits for the above platforms. Special attention will be paid to the design of efficient schemes for quantum error correction, which is the key enabling tool for scalable quantum computing. The newly designed quantum gates will be used to implement optimized quantum circuits for entire quantum algorithms, such as Grover search. All these elements of quantum computing will be experimentally tested on IBM Quantum and other quantum computers if such become available during the project.
WP3 contains several groups of closely related tasks. The first is quantum gate tomography, i.e. full characterization of high-fidelity quantum gates. The problem here is that for high-fidelity quantum gates the errors are extremely small, much less than 1%. It is very important to determine how small this error is because a set of quantum gates with an error of less than 0.01% are ideally suitable for scalable quantum computing, whereas errors of 0.1% require sophisticated error correction protocols, and errors over 1% render the quantum gates unsuitable for quantum computing. It is a difficult task to determine how small the error is from an experimental viewpoint because an efficiency of 99.99% is indiscernible from 99.9%, or even 99%. The idea here is to repeat the quantum gate N times because quantum errors scale as N2, i.e. much faster than classical errors which pile up as N. When amplified to large values, the error can be measured accurately. The second group of tasks is related to closely related problems of subwavelength spatial localization and characterisation of quantum motion near zero temperature. The third group of tasks is related to quantum sensing of small frequency shifts, caused, e.g. by small electric or magnetic fields. This problem will be tackled in two ways. In one of them, a similar approach as the error amplification of the quantum gates will be used – by repeated interactions which greatly amplify the effects of these small shifts. In the other, an appropriate quantum phase transition will be used, which is very sensitive to small variations of experimental parameters.
WP4 This WP uses similar ideas as one of the approaches of WP3: quantum phase transition in quantum many-body systems. One of the main tasks here is to investigate the influence of the external environment on the precision of the measurement. Such an open quantum system can lead to a reduction in the signal-to-noise ratio. Remarkably, the use of system-environment interaction may lead to enhancement of the sensitivity of parameter estimation due to the onset of dissipative phase transition. The other task is to study a quantum phase transition in quantum many-body systems which can be simulated by using various quantum-optical platforms. An important connection is that between quantum phase transition and quantum chaos and respectively the transition to equilibrium and quantum thermalization in isolated quantum systems. To this end, we will extend this research to quantum models which can be efficiently simulated in experimentally controllable quantum-optical systems. We also plan to develop methods for quantum simulation of open quantum systems which show dissipative phase transition. Such a transition occurs due to the balance between the coherent pump and dissipative losses. The other research task is to propose quantum simulation of interacting bosonic models which are described by a nonlinear Hamiltonian. One such system where a nonlinear interaction between bosons can be realized is an ion crystal in a Paul trap. In this task, we plan to study the emergence of novel quantum phase transitions which show a non-Gaussian behavior around the critical point and the onset of quantum chaos, and transition to equilibration in finite-size non-linear bosonic models.
WP5 will investigate spectra of alkaline, alkaline-earth diatomic molecules11 and multi-atom chiral molecules. The research goal of WP5 is developing further the CC treatment of diatomic molecules, starting from the experiment for collecting experimental data and ending with the CC model, able to reproduce all experimental observations, including their hyperfine structure (HFS). Finally, within WP5 we will develop a new method for the detection of chiral molecules based on the quantum control approaches from WP1.
WP6 Using the ideas of adiabatic evolution and composite pulses, which were specifically developed in quantum physics, we are going to apply them in classical optics to have novel and robust optical devices. One such gadget is a novel, simpler-to-use polarization controller that uses the same optical components as Messaadi's polarization rotator, but in a different wave plate arrangement. Another device is an arbitrary nonreciprocal polarization rotator, which is constructed using two nonreciprocal half-wave plates.
The interconnections between the research Work Packages are illustrated in the chart. WP1 is the unifying approach to all other WPs. There is a very close link between WP2 and WP3 because the quantum gate tomography in WP3 is crucial for the quantum computing elements. Furthermore, the concept of quantum phase transition links WP3 and WP4, which feed one another with ideas and results. WP6 is also tightly linked to WP1 because it develops novel optical devices based on analogy with quantum control tools; on the other hand, it may happen that concepts in classical optics might be useful in quantum control as well. WP5 is linked to both WP1 and WP6 because control of molecular states rely on sophisticated quantum control methods.
In case some of the expected results are not achieved mitigation measure will be implemented. For example, if machine learning quantum control methods are not delivered in WP1, the well-established adiabatic and composite methods will be used in WP2, WP3 and WP6. In another example, if methods based on critical quantum systems (from WP4) to measure weak magnetic fields, electric forces and frequencies in WP3 fail, we will develop alternative methods based on coherent amplification of errors from WP1. Furthermore, if new tomography methods in WP3 prove inefficient, we will resort to the existing methods of randomized benchmarking to characterize the quantum gates in WP2. Finally, if methods for chiral resolution with four-level systems in WP5 fail, we will use adiabatic and composite methods from WP1 in systems with more levels.