Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expectation Values from the Single-Layer Quantum Approximate
  Optimization Algorithm on Ising Problems   We report on the energy-expectation-value landscapes produced by the
single-layer ($p=1$) Quantum Approximate Optimization Algorithm (QAOA) when
being used to solve Ising problems. The landscapes are obtained using an
analytical formula that we derive. The formula allows us to predict the
landscape for any given Ising problem instance and consequently predict the
optimal QAOA parameters for heuristically solving that instance using the
single-layer QAOA. We have validated our analytical formula by showing that it
accurately reproduces the landscapes published in recent experimental reports.
We then applied our methods to address the question: how well is the
single-layer QAOA able to solve large benchmark problem instances? We used our
analytical formula to calculate the optimal energy-expectation values for
benchmark MAX-CUT problems containing up to $7\,000$ vertices and $41\,459$
edges. We also calculated the optimal energy expectations for general Ising
problems with up to $100\,000$ vertices and $150\,000$ edges. Our results
provide an estimate for how well the single-layer QAOA may work when run on a
quantum computer with thousands of qubits. In addition to providing performance
estimates when optimal angles are used, we are able to use our analytical
results to investigate the difficulties one may encounter when running the QAOA
in practice for different classes of Ising instances. We find that depending on
the parameters of the Ising Hamiltonian, the expectation-value landscapes can
be rather complex, with sharp features that necessitate highly accurate
rotation gates in order for the QAOA to be run optimally on quantum hardware.
We also present analytical results that explain some of the qualitative
landscape features that are observed numerically.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th