Ulysse Chabaud

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The approximate coherent state rank is the minimal number of (classical) coherent states required to approximate a continuous-variable bosonic quantum state and directly relates to the classical complexity of simulating bosonic computations. Despite its importance, little is known about lower bounds on this quantity, even for basic families of states. In this talk, I will present the first nontrivial lower bounds on the approximate coherent state rank, both in the single-mode and multimode cases. In the former case, I will use tools from low-rank approximation theory. In the latter case, I will exploit a connection with the algebraic complexity of the permanent. These results establish an unconditional barrier to efficient classical simulation of Boson Sampling via coherent state decompositions and connect non-classicality of bosonic quantum systems to central questions in algebraic complexity.
Based on arXiv:2604.00766, joint work with Florian Cottier.

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INRIA Paris
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Contact: Markus Heinrich