Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A framework for optimal quantum spatial search using alternating
  phase-walks   We present a novel methodological framework for quantum spatial search,
generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating
applications of marked-vertex phase shifts and continuous-time quantum walks.
We determine closed form expressions for the optimal walk time and phase shift
parameters for periodic graphs. These parameters are chosen to rotate the
system about subsets of the graph Laplacian eigenstates, amplifying the
probability of measuring the marked vertex. The state evolution is
asymptotically optimal for any class of periodic graphs having a fixed number
of unique eigenvalues. We demonstrate the effectiveness of the algorithm by
applying it to obtain $\mathcal{O}(\sqrt{N})$ search on a variety of graphs.
One important class is the $n \times n^3$ rook graph, which has $N=n^4$
vertices. On this class of graphs the $\mathcal{CG}$ algorithm performs
suboptimally, achieving only $\mathcal{O}(N^{-1/8})$ overlap after time
$\mathcal{O}(N^{5/8})$. Using the new alternating phase-walk framework, we show
that $\mathcal{O}(1)$ overlap is obtained in $\mathcal{O}(\sqrt{N})$ phase-walk
iterations.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph