Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian
  assisted with an ancillary qubit system   We propose a quantum algorithm to obtain the lowest eigenstate of any
Hamiltonian simulated by a quantum computer. The proposed algorithm begins with
an arbitrary initial state of the simulated system. A finite series of
transforms is iteratively applied to the initial state assisted with an
ancillary qubit. The fraction of the lowest eigenstate in the initial state is
then amplified up to $\simeq 1$. We prove that our algorithm can faithfully
work for any arbitrary Hamiltonian in the theoretical analysis. Numerical
analyses are also carried out. We firstly provide a numerical
proof-of-principle demonstration with a simple Hamiltonian in order to compare
our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently
proposed in [Nature Photonics 8, 113 (2014)]. The result shows a good agreement
with our theoretical analysis, exhibiting the comparable behavior to the best
"cooling" with the DLAC method. We then consider a random Hamiltonian model for
further analysis of our algorithm. By numerical simulations, we show that the
total number $n_c$ of iterations is proportional to $\simeq {\cal
O}(D^{-1}\epsilon^{-0.19})$, where $D$ is the difference between the two lowest
eigenvalues, and $\epsilon$ is an error defined as the probability that the
finally obtained system state is in an unexpected (i.e. not the lowest)
eigenstate.

18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con