PARITY is the problem of determining the parity of a string f of n bits given access to an oracle that responds to a query x ∈ {0, 1, . . . , n − 1} with the x bit of the string, f(x). Classically, n queries are required to succeed with probability greater than 1/2 (assuming equal prior probabilities for all length n bitstrings), but only ⌈n/2⌉ quantum queries suffice to determine the parity with probability 1. We consider a generalization to strings f of n elements of Zk and the problem of… CONTINUE READING

Quantum lower bounds by polynomials ” On the power of quantum computation ” A subexponential - time quantum algorithm for the dihedral hidden subgroup problem ” , quant - ph / 0302112