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Quantum Approximate Optimization Algorithm (QAOA) is studied primarily tofind approximate solutions to combinatorial optimization problems. For a graphwith $n$ vertices and $m$ edges, a depth $p$ QAOA for the Max-cut problemrequires $2\cdot m \cdot p$ CNOT gates. CNOT is one of the primary sources oferror in modern quantum computers. In this paper, we propose two hardwareindependent methods to reduce the number of CNOT gates in the circuit. First,we present a method based on Edge Coloring of the input graph that minimizesthe the number of cycles (termed as depth of the circuit), and reduces upto$\lfloor \frac{n}{2} \rfloor$ CNOT gates. Next, we depict another method basedon Depth First Search (DFS) on the input graph that reduces $n-1$ CNOT gates,but increases depth of the circuit moderately. We analytically derive thecondition for which the reduction in CNOT gates overshadows this increase indepth, and the error probability of the circuit is still lowered. We show thatall IBM Quantum Hardware satisfy this condition. We simulate these two methodsfor graphs of various sparsity with the \textit{ibmq\_manhattan} noise model,and show that the DFS based method outperforms the edge coloring based method,which in turn, outperforms the traditional QAOA circuit in terms of reductionin the number of CNOT gates, and hence the probability of error of the circuit.

Optimizing Ansatz Design in QAOA for Max-cut