A remarkable consequence of spontaneously breaking the time translational symmetry in a system, is the emergence of time crystals. In periodically driven systems, discrete time crystals (DTC) can be realized which have a periodicity that is n times the driving period. However, all of the experimental observations have been performed for period-doubling and period-tripling DTC. Novel physics can arise by simulating many-body physics in the time domain, which would require a genuine realisation of the n-tupling DTC. A system of ultra-cold bosonic atoms bouncing resonantly on an oscillating mirror is one of the models that can realise large period DTC. The preparation of DTC demands control in creating the initial distribution of the ultra-cold bosonic atoms along with the mirror frequency. In this work, we demonstrate that such DTC is robust against perturbations to the initial distribution of atoms. We show how Bayesian methods can be used to enhance control in the preparation of the initial state as well as to efficiently calculate the phase diagram for such a model. Moreover, we examine the stability of DTCs by analyzing quantum many-body fluctuations and show that they do not reveal signatures of heating.

This paper proposes a nonlinear finite-time converging observer for a class of nonlinear systems. The estimate is recovered from the present and delayed estimates provided by two independent dynamical systems converging to a function of the state with linear error dynamics. The estimation is carried out using only the Jacobian matrix of both transformations determined by solving two systems of partial derivative equations. The results are illustrated on a bioreactor model.

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We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.