We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C2Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C2Z gates.

We study the 2×2 charge density wave (CDW) in epitaxially-grown monolayer TiSe2. Our temperaturedependent angle-resolved photoemission spectroscopy measurements indicate a strong-coupling instability, but reveal how not all states couple equally to the symmetry-breaking distortion, with an electron pocket persisting to low temperature as a non-bonding state. We further show how the CDW order can be suppressed by a modest doping of around 0.06(2) electrons per Ti. Our results provide an opportunity for quantitative comparison with a realistic tight-binding model, which emphasises a crucial role of structural aspects of the phase transition in understanding the hybridisation in the ground state. Together, our work provides a comprehensive understanding of the phenomenology of the CDW in TiSe2 in the 2D limit.

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