Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum homeopathy works: Efficient unitary designs with a system-size
  independent number of non-Clifford gates   Many quantum information protocols require the implementation of random
unitaries. Because it takes exponential resources to produce Haar-random
unitaries drawn from the full $n$-qubit group, one often resorts to
$t$-designs. Unitary $t$-designs mimic the Haar-measure up to $t$-th moments.
It is known that Clifford operations can implement at most $3$-designs. In this
work, we quantify the non-Clifford resources required to break this barrier. We
find that it suffices to inject $O(t^{4}\log^{2}(t)\log(1/\varepsilon))$ many
non-Clifford gates into a polynomial-depth random Clifford circuit to obtain an
$\varepsilon$-approximate $t$-design. Strikingly, the number of non-Clifford
gates required is independent of the system size -- asymptotically, the density
of non-Clifford gates is allowed to tend to zero. We also derive novel bounds
on the convergence time of random Clifford circuits to the $t$-th moment of the
uniform distribution on the Clifford group. Our proofs exploit a recently
developed variant of Schur-Weyl duality for the Clifford group, as well as
bounds on restricted spectral gaps of averaging operators.

3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph