Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simulating quantum computers with probabilistic methods   We investigate the boundary between classical and quantum computational
power. This work consists of two parts. First we develop new classical
simulation algorithms that are centered on sampling methods. Using these
techniques we generate new classes of classically simulatable quantum circuits
where standard techniques relying on the exact computation of measurement
probabilities fail to provide efficient simulations. For example, we show how
various concatenations of matchgate, Toffoli, Clifford, bounded-depth, Fourier
transform and other circuits are classically simulatable. We also prove that
sparse quantum circuits as well as circuits composed of CNOT and exp[iaX] gates
can be simulated classically. In a second part, we apply our results to the
simulation of quantum algorithms. It is shown that a recent quantum algorithm,
concerned with the estimation of Potts model partition functions, can be
simulated efficiently classically. Finally, we show that the exponential
speed-ups of Simon's and Shor's algorithms crucially depend on the very last
stage in these algorithms, dealing with the classical postprocessing of the
measurement outcomes. Specifically, we prove that both algorithms would be
classically simulatable if the function classically computed in this step had a
sufficiently peaked Fourier spectrum.

32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat