  High error rates and limited fidelity of quantum gates in near-term quantum
devices are the central obstacles to successful execution of the Quantum
Approximate Optimization Algorithm (QAOA). In this paper we introduce an
application-specific approach for mitigating the errors in QAOA evolution by
leveraging the symmetries present in the classical objective function to be
optimized. Specifically, the QAOA state is projected into the
symmetry-restricted subspace, with projection being performed either at the end
of the circuit or throughout the evolution. Our approach improves the fidelity
of the QAOA state, thereby increasing both the accuracy of the sample estimate
of the QAOA objective and the probability of sampling the binary string
corresponding to that objective value. We demonstrate the efficacy of the
proposed methods on QAOA applied to the MaxCut problem, although our methods
are general and apply to any objective function with symmetries, as well as to
the generalization of QAOA with alternative mixers. We experimentally verify
the proposed methods on an IBM Quantum processor, utilizing up to 5 qubits.
When leveraging a global bit-flip symmetry, our approach leads to a 23% average
improvement in quantum state fidelity.
