One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algo...
We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of...
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of Ç´ÐÓ Ò · ÐÓ ÐÓ ´½ µµ on the circuit depth for computin...
We introduce two new complexity measures for Boolean functions, which we name sumPI and maxPI. The quantity sumPI has been emerging through a line of research on quantum query com...
We give a tight lower bound of ( n) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communica...