Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commuting quantum circuits: efficient classical simulations versus
  hardness results   The study of quantum circuits composed of commuting gates is particularly
useful to understand the delicate boundary between quantum and classical
computation. Indeed, while being a restricted class, commuting circuits exhibit
genuine quantum effects such as entanglement. In this paper we show that the
computational power of commuting circuits exhibits a surprisingly rich
structure. First we show that every 2-local commuting circuit acting on d-level
systems and followed by single-qudit measurements can be efficiently simulated
classically with high accuracy. In contrast, we prove that such strong
simulations are hard for 3-local circuits. Using sampling methods we further
show that all commuting circuits composed of exponentiated Pauli operators
e^{i\theta P} can be simulated efficiently classically when followed by
single-qubit measurements. Finally, we show that commuting circuits can
efficiently simulate certain non-commutative processes, related in particular
to constant-depth quantum circuits. This gives evidence that the power of
commuting circuits goes beyond classical computation.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys