Beatriz Cardoso Dias, PhD at TUM Mathematics Department, will give a talk. Everybody is cordially invited to attend:
https://www.math.cit.tum.de/math/forschung/gruppen/quantum-information-theory/
Title: Rank-based methods for classical simulation of fermionic and bosonic non-Gaussian circuits
Abstract: Rank-based methods for classical simulation of quantum computations are
suitable for simulating Clifford circuits with few magic states or magic
gates. We adapt these methods to simulate Gaussian circuits with few
non-Gaussian resources, both in the fermionic and the bosonic settings.
Instead of relying on the stabilizer formalism, our methods build on the
covariance matrix formalism for Gaussian computations. Our algorithms
have polynomial runtime in the number of modes, the size of the circuit,
and magic monotones — the rank and extent — which quantify the degree of
non-Gaussianity of the initial state. We give an overview of the key
ingredients used in rank-based computations, whether the underlying free
theory is stabilizer or fermionic/bosonic Gaussian computations: a
minimal extension of the free theory that keeps track of phases in
superpositions of Gaussian states, the ability to compute overlaps
between free states. In the second part of the talk we give a
probabilistic algorithm that samples from the distribution of outcomes
when measuring a superposition of free states, with runtime linear in
the number of terms in the superposition. The algorithm uses samples
from the distribution of outcomes when measuring free states, and oracle
access to the probability density functions of the involved
distributions. This algorithm gives a new reduction from strong
simulations (the problem of computing probabilities) to weak simulating
(the problem of sampling) particularly relevant in the case of
continuous outcome measurements. It extends the strong simulation
algorithms of Phys. Rev. A 110, 042402 to weak simulation.