A quantum lower bound for the query complexity of Simon's problem

Pascal Koiran; Vincent Nesme; Natacha Portier

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A quantum lower bound for the query complexity of Simon's problem

Pascal Koiran·Vincent Nesme·Natacha Portier

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Abstract

Simon in his FOCS'94 paper was the first to show an exponential gap between classical and quantum computation. The problem he dealt with is now part of a well-studied class of problems, the hidden subgroup problems. We study Simon's problem from the point of view of quantum query complexity and give here a first nontrivial lower bound on the query complexity of a hidden subgroup problem, namely Simon's problem. Our bound is optimal up to a constant factor.

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Pascal Koiran, Vincent Nesme, Natacha Portier. 2005-01-12. A quantum lower bound for the query complexity of Simon's problem. https://arxiv.org/abs/quant-ph/0501060

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