Constructing Arbitrary Single-Particle Unitaries for Digital Quantum Simulators

Alexander Roth

Abstract

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A major challenge in neutral-atom quantum simulation is control. Our experimental tools are local, allowing us to “talk to” one or two atoms, but developed algorithms demand complex global operations. How can we bridge this gap? In this talk, I’ll present a systematic description for compiling any desired global, single-particle operation into a practical sequence of simple local “tunneling” and “phase-shift” gates. I’ll then show this recipe in action for two key examples: the Discrete Fourier Transform (DFT) and parallel atom sorting. We will see how to extend these ideas to two dimensions, resulting in a 2D atom rearrangement protocol that scales sub-linearly with the total number of atoms. This provides a solution to a major bottleneck for scaling up these quantum platforms.