Lower Bounds on Quantum Query Complexity for Read-Once Formulas with XOR and MUX Operators

2010 IEICE transactions on information and systems  
We introduce a complexity measure r for the class F of read-once formulas over the basis {AND, OR, NOT, XOR, MUX} and show that for any Boolean formula F in the class F , r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in F , the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f . Thus, the paper gives further evidence for
more » ... e conjecture that there is an only quadratic gap for all functions. key words: quantum query complexity, read-once formulas, decision trees, adversary method
doi:10.1587/transinf.e93.d.280 fatcat:ruoeckb2nfaw5ghwvosteh6ftm