Affiliation:
1. USRA Research Institute for Advanced Computer Science
2. KBR, Inc.
Abstract
We introduce a framework for simulating quantum optics by decomposing
the system into a finite rank (number of terms) superposition of
coherent states. This allows us to define a resource theory, where
linear optical operations are “free” (i.e., do not increase the rank),
and the simulation complexity for an m-mode system scales quadratically in m, in stark contrast to the Hilbert space dimension. We
outline this approach explicitly in the Fock basis, relevant in
particular for Boson sampling, where the simulation time (space)
complexity for computing output amplitudes, to arbitrary accuracy,
scales as O(m2 2
n
)
[O(m2
n
)] for n photons distributed among m modes. We additionally demonstrate that linear optical
simulations with the n photons initially
in the same mode scales efficiently, as O(m2 n). This paradigm provides a practical notion of
“non-classicality,” i.e., the classical resources required for
simulation. Moreover, by making connections to the stellar rank
formalism, we show this comes from two independent contributions, the
number of single-photon additions and the amount of squeezing.
Funder
Defense Advanced Research Projects
Agency
KBR Prime
NASA
Cited by
4 articles.
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