Armando Angrisani

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Classically simulating arbitrary quantum dynamics is widely believed to be intractable. Yet in structured settings, specialized classical methods can succeed. Recent work has shown that many families of quantum dynamics admit accurate low-degree approximations: by expanding observables or states in a suitable operator basis (e.g., Pauli, Majorana, or displacement operators) and truncating to low degree, one obtains a new class of classical simulation methods—propagation-based algorithms. This closely parallels developments in classical learning theory on low-degree approximations of Boolean functions.
The resulting guarantees typically rest on several ingredients, including bounded magic, local noise, randomness in the gate set, or distributional properties such as anticoncentration. In this talk, we survey a series of our recent results applying propagation-based algorithms to both noisy and noiseless circuits, and we discuss extensions of these ideas to continuous-variable quantum dynamics.

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EPFL
0.02
Contact: Markus Heinrich