Quantum algorithms promise an immense improvement to our current information processing capabilities by utilizing interference phenomena in an exponentially large Hilbert space. However, the large size of the Hilbert space also poses a crucial challenge to the experimentalists, who strive to design protocols that navigate the Hilbert space using only a small number of semiclassical control fields.

In this talk, we propose concrete protocols to implement a framework of quantum algorithms on the experimental platform of Rydberg atoms [Sina Zeytinoglu and Sho Sugiura, arXiv:2201.04665]. What enables such an overarching proposal is the recently developed algorithms of Linear Combination of Unitaries (LCU) and Quantum Signal Processing (QSP), which was shown to unify core quantum subroutines such as phase estimation, search and Hamiltonian simulation. We aim to perform a comprehensive study of the implementation of these quantum algorithms in the Rydberg system. Specifically, we (1) identify the tree structure of the data to be loaded into the Rydberg system, (2) give the complete procedure to load the data into the Rydberg system and perform the calculation down to the laser pulse sequences, and (3) analyze the errors this procedure and show that it achieves a near-optimal implementation of the target algorithm, (4) develop a method to make the experimental system scalable with respect to the system size, and (5) calculate the resources required to run an optimal Hamiltonian simulation on the Rydberg system.

While these results are specific to the Rydberg platform, our results highlight the importance of including the details of the native dynamics relevant to a concrete experimental implementation when analysing the performance of quantum algorithms.

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