We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium 87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum simulation experiments with SU(N)-symmetric matter. By controlling the resonance conditions of Raman transitions with a tensor light shift, we can perform rotations within a restricted Hilbert space of two isolated spin states among the 2F+1 = 10 possible states. These manipulations correspond to engineering unitary operations deriving from generators of the SU(N) algebra beyond what can be done by simple spin precession. We present Ramsey interferometers involving an isolated pair of Zeeman states with no measurable decoherence after 3 seconds. We also demonstrate that one can harvest the large spin degrees of freedom as a qudit resource by implementing two interferometer schemes over four states. The first scheme senses in parallel multiple external fields acting on the atoms, and the second scheme simultaneously measures multiple observables of a collective atomic state - including non-commuting ones. Engineering unitary transformations of the large spin driven by other generators than the usual spin-F representation of the SU(2) group offers new possibilities from the point of view of quantum metrology and quantum many-body physics, notably for the quantum simulation of large-spin SU(N)-symmetric quantum magnetism with fermionic alkaline-earth atoms.

In quantum mechanics, the probability distribution function (PDF) and full counting statistics (FCS) play a fundamental role in characterizing the fluctuations of quantum observables, as they encode the complete information about these fluctuations. In this letter, we measure these two quantities in a trapped-ion quantum simulator for the transverse and longitudinal magnetization within a subsystem. We utilize the toolbox of classical shadows to postprocess the measurements performed in random bases. The measurement scheme efficiently allows access to the FCS and PDF of all possible operators on desired choices of subsystems of an extended quantum system.

Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading datasets (both classical and quantum) onto the quantum processor. However, a realization of this fundamental building block is still outstanding, since existing proposals require prohibitively many resources for reliable implementations, or are not compatible with current architectures. Moreover, present approaches cannot be scaled-up, as they do not allow for efficient quantum error-correction. Here we develop a QRAM design, that enables fast and robust QRAM calls, naturally allows for fault-tolerant and error-corrected operation, and can be integrated on present hardware. Our proposal employs a special quantum resource state that is consumed during the QRAM call: we discuss how it can be assembled and processed efficiently in a dedicated module, and give detailed blueprints for modern neutral-atom processors. Our work places a long missing, fundamental component of quantum computers within reach of currently available technology; this opens the door to algorithms featuring practical quantum advantage, including search or oracular problems, quantum chemistry and machine learning.