Inverting a permutation is as hard as unordered search

We describe a reduction from the problem of unordered search (with a unique solution) to the problem of inverting a permutation. Since there is a straightforward reduction in the reverse direction, the problems are essentially equivalent. The reduction helps us bypass the Bennett-Bernstein-Brassard-Vazirani hybrid argument [2] and the Ambainis quantum adversary method [1] that were earlier used to derive lower bounds on the quantum query complexity of the problem of inverting permutations. It directly implies that the quantum query complexity of the problem is in ( n ).

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Ashwin Nayak
• Keywords: Ambainis Quantum Adversary, CORR 2010, Education, Quantum Query Complexity, Unordered Search