We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω n1/3 /w queries to f, even if the algorith...
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progres...
We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particu...
— The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention...
Vivek V. Shende, Stephen S. Bullock, Igor L. Marko...
We improve upon indirect diagonalization arguments for lower bounds on explicit problems within the polynomial hierarchy. Our contributions are summarized as follows.