WP1 (1.1-1.3) Ultrahigh fidelity robust quantum gates will be designed by using advanced quantum control methods, including adiabatic (1.1) and composite (1.2) methods as well as machine learning (1.3), and will be adapted to superconducting and trapped-ion qubits. In particular, brand-new composite sequences in which both the carrier frequency and the phase of each constituent pulse will be used as control parameters. (1.4) Qudit gates, involving d states, will be developed by using resonant, adiabatic or composite approaches and the most suitable linkages will be determined. (1.5) Novel dynamical decoupling sequences will be constructed, which outperform the existing ones by using composite approaches for quantum gate engineering. Inverted dynamical decoupling sequences for decoherence characterisation will be explored.
WP2 Theoretical development of high-fidelity (2.1) single-qubit gates (X, H, Rz) and (2.2) two-qubit gates (CNOT, CPhase, cross-resonance, iSWAP, or bSWAP) in superconducting and trapped-ion architectures will be conducted by more precise calibration routines, reducing the dominant sources of error (such as pulse imperfections, population leakage, cross-talk, parasitic interactions), and composite error correction. These gates will be used to build (2.3) optimized quantum circuits, e.g., for the quantum Fourier transform, the Toffoli or Fredkin gates. (2.4) The high-fidelity gates will be used to demonstrate a quantum algorithm, e.g. the Grover search. Experimental demonstration of the proposed methods will be conducted using the cloud-based IBM Quantum processors, whenever this is allowed by the available IBM systems.
WP3 (3.1) Fast and efficient tomographic methods will be developed for precise characterization of single-qubit and two-qubit quantum gates. The methods will be experimentally tested on IBM Quantum. (3.2) New methods for spatial localization will be developed and demonstrated on doped solids. One of these will use narrowband composite pulses and the other Stark shifting Laguerre-Gaussian or Bessel laser beams. (3.3) A small parameter that breaks the symmetry of a quantum system around the transition point can be measured with great precision. We will develop methods based on critical quantum systems to measure weak magnetic fields, electric forces and frequencies. (3.4) Measuring micro Kelvin temperatures is of key importance for improving the precision of quantum gates. We will develop new efficient techniques for measuring the temperature of a quantum oscillator. One of these will be based on transferring temperature information onto the collective spin states of the qubits, and the other on using narrowband composite pulses.
WP4 (4.1) We will develop sensing techniques in open quantum systems where the presence of a dissipative phase transition improves the sensitivity of parameter estimation, which will allow the construction of stable quantum sensors for magnetic fields and electric forces. (4.2) We will study a quantum phase transition in a spin-boson model of an interacting ensemble of spin-½ particles with bosonic modes, the onset of a quantum phase transition and the emergence of quantum chaos and thermalization in such many-body spin-boson models. (4.3) We will study the onset of dissipative phase transitions in open quantum systems which can be efficiently simulated with quantum-optical systems. (4.4) We will develop methods for quantum simulation of nonlinear boson models. We will study the emergence of novel quantum phase transitions in finite-size bosonic models.
WP5 Within the project we will study the HFS structure of the c3Sigma+ state in KRb (5.1), apply the CC approach to various band systems (also with HFS) and will determine empirical potential curves and off-diagonal matrix elements which reproduce the line frequencies within their uncertainty (5.2). We will include the line intensities as experimental data and we will extract information on the transition dipole moment (5.3). In this way we will have at our disposal model functions, capable of predicting energies of mixed quantum states, their composition and transition probabilities. (5.4) Finally, we will develop a new method for chiral resolution of molecules by using quantum systems with more than three states.
WP6. (6.1) Using standard frequency conversion techniques, one could achieve either complete frequency conversion for a very narrowband spectrum or inefficient conversion for broad bandwidth. We will construct composite nonlinear crystals to overcome these limitations. (6.2) The polarization manipulation of light is done mainly with polarizers, wave plates or/and polarization rotators, or combinations of them. They suffer from being narrowband, slow, or big in size. We will develop new and better polarization manipulation devices. (6.3) There are different methods for the design of optical multilayer coatings. The coating performance is improved by a numerical evolutionary algorithm combined with random local searches. We will develop a robust analytical approach to optimize a series of thin-film layers. (6.4) A non-reciprocal wave retarder based on a combination of reciprocal and non-reciprocal polarization rotators in between two quarter-wave plates was demonstrated recently. However, it is not broadband. We will use a composite setup of several non-reciprocal wave plates to achieve a broadband non-reciprocal wave retarder.
WP7. The project website will be created and running from the beginning of the project. Regular project meetings, with presentations on each WP, will be held: 3 in the first period and 3 in the second period. One public lecture for the general audience will be delivered each year.
The duration of all WPs is from M1 to M2, but the Tasks within them are timed such that they allow for efficient interconnections between the WPs. For example, tasks T1.1 and T1.2 are timed in the first half of the project because they will feed research on WP2, WP3, WP5, and WP6. For this reason, Tasks T2.3, T2.4, T3.3, T3.4, T5.4, T6.1 and T6.3 are delayed toward the second half of the project, waiting the results a of WP1. Likewise, task T3.1 which will be used in Tasks T2.1 and T2.2 of WP2, is scheduled in the first half of the project too. Similarly, Tasks T2.1 and T2.2 precede T2.3 and T2.4, in order to feed them with their results.