A lower bound on the quantum query complexity of read-once functions [article]

Howard Barnum, Michael Saks
2002 arXiv   pre-print
We establish a lower bound of Ω(√(n)) on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that Ω(√(D(f))) is a lower bound for all Boolean functions. Our technique extends a result of Ambainis, based on the idea that successful computation of a function requires "decoherence" of initially coherently superposed inputs in the query register, having different values of the function. The number of queries is bounded by comparing the
more » ... uired total amount of decoherence of a judiciously selected set of input-output pairs to an upper bound on the amount achievable in a single query step. We use an extension of this result to general weights on input pairs, and general superpositions of inputs.
arXiv:quant-ph/0201007v1 fatcat:an663syfufdc7pzzt2xpwldcbe