Analysis of Quantum Approximate Optimization Algorithm under Realistic
  Noise in Superconducting Qubits
The quantum approximate optimization algorithm (QAOA) is a promising
quantum-classical hybrid technique to solve combinatorial optimization problems
in near-term gate-based noisy quantum devices. In QAOA, the objective is a
function of the quantum state, which itself is a function of the gate
parameters of a multi-level parameterized quantum circuit (PQC). A classical
optimizer varies the continuous gate parameters to generate distributions
(quantum state) with significant support to the optimal solution. Even at the
lowest circuit depth, QAOA offers non-trivial provable performance guarantee
which is expected to increase with the circuit depth. However, the existing
analysis fails to consider non-idealities in the qubit quality i.e., short
lifetime and imperfect gate operations in realistic quantum hardware. In this
article, we investigate the impact of various noise sources on the performance
of QAOA both in simulation and on a real quantum computer from IBM. Our
analyses indicate that the optimal number of stages (p-value) for any QAOA
instance is limited by the noise characteristics (gate error, coherence time,
etc.) of the target hardware as opposed to the current perception that
higher-depth QAOA will provide monotonically better performance for a given
problem compared to the low-depth implementations.
Mahabubul Alam Abdullah Ash-Saki Swaroop Ghosh