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We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.more » « less
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Herrman, Rebekah ; Treffert, Lorna ; Ostrowski, James ; Lotshaw, Phillip C. ; Humble, Travis S. ; Siopsis, George ( , Quantum Information Processing)
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Ramshani, Mohammad ; Li, Xueping ; Khojandi, Anahita ; Treffert, Lorna ( , Proceedings of the 2019 Winter Simulation Conference)