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Simon's problem is to find a hidden period (a bitstring) encoded into anunknown 2-to-1 function. It is one of the earliest problems for which anexponential quantum speedup was proven for ideal, noiseless quantum computers,albeit in the oracle model. Here, using two different 127-qubit IBM Quantumsuperconducting processors, we demonstrate an algorithmic quantum speedup for avariant of Simon's problem where the hidden period has a restricted Hammingweight. The speedup is sub-exponential and is enhanced when the computation isprotected by dynamical decoupling to suppress decoherence. The speedup isfurther enhanced with measurement error mitigation. This constitutes ademonstration of a bona fide quantum advantage for an Abelian hidden subgroupproblem.

Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem