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IEEE Nexo-Tech International Conference on Advanced Technologies and Innovations (ICATI)

Quantum Approximate Optimization Algorithm (QAOA) for Solving NP-Hard Problems

Srikanth Kilaru, Thota Sravya Vardhani, Attluri Udaya Lakshmi, Kota Mounika, Thotakura Gnana Prasuna

Published May 8, 2026• 0 citations
Publisher
DOI
10.1109/icati69399.2026.11604476

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Quantum Approximate Optimization algorithm (QAOA) is one of the candidates to achieve a near-term quantum advantage. As QAOA seems only capable of solving optimization problems, there is a folklore that QAOA cannot see the difference between easy problems such as 2-SAT and hard problems such as 3-SAT -- although 2-SAT is in the polynomial-time (P) class, its optimization version is also nondeterministic polynomial-time (NP)-hard. In this paper, we show that the folklore is not true. We find a computational phase transition in QAOA when solving a variant of 3-SAT -- the amplitude of gradient and the success probability achieve their minimum at the well-known SAT-UNSAT phase transition. On the contrary, for 2-SAT, such a phenomenon is absent at SAT-UNSAT phase transition and the success probability is unity for a reasonable circuit depth. We connect the gradient transition to the dynamical Lie algebra of the QAOA circuit. In solving the NP-hard optimization versions of SAT, we identify quantum advantages over a classical approximate algorithm at quite a shallow depth of p=4p=4p=4 for the problem size of n=10n=10n=10.
Timetabling is an NP-Hard problem that searches for periodic scheduling of events that must meet a set of hard and soft constraints. Because of the difficulty in finding an exact solution, the use of heuristics to address the problem is a common practice. When only the hard constraints are considered, the timetabling problem can be reduced to graph vertex coloring. This similarity between both problems has motivated the use of graph coloring heuristics as a means to solve the timetabling problem. We propose the use of the Quantum Approximate Optimization Algorithm as a heuristic to solve the school timetabling problem. The QAOA is a hybrid quantum-classical algorithm that can be used to address combinatorial optimization problems. We simulated QAOA in a minimal example with 42 qubits using the Ket Quantum Programming Language and our results showed that it is possible to apply QAOA to the school timetabling problem.
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