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Results are presented for an adiabatic quantum algorithm to compute low peak sidelobe binary and unimodular codes on a D-Wave 2 quantum computer. The quantum algorithm is benchmarked against a conventional genetic algorithm (GA). The quantum algorithm shows roughly a 100 times speedup relative to the GA for binary codes longer that 100 bits and is capable of producing low sidelobe binary codes up to length 426 on the current D-Wave 2 hardware. Results are presented for Doppler tolerant binary and quad-phase codes computed using the same quantum algorithm.