Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient unitary designs with nearly time-independent Hamiltonian
  dynamics   We provide new constructions of unitary $t$-designs for general $t$ on one
qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of
which dynamics always forms a unitary design after a threshold time, as a basic
framework to investigate randomising time evolution in quantum many-body
systems. The new constructions are based on recently proposed schemes of
repeating random unitaires diagonal in mutually unbiased bases. We first show
that, if a pair of the bases satisfies a certain condition, the process on one
qudit approximately forms a unitary $t$-design after $O(t)$ repetitions. We
then construct quantum circuits on $N$ qubits that achieve unitary $t$-designs
for $t = o(N^{1/2})$ using $O(t N^2)$ gates, improving the previous result
using $O(t^{10}N^2)$ gates in terms of $t$. Based on these results, we present
a design Hamiltonian with periodically changing two-local spin-glass-type
interactions, leading to fast and relatively natural realisations of unitary
designs in complex many-body systems.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom