In this paper, we give a lower bound of (n(d-1)/2 ) on the quantum query complexity for finding a fixed point of a discrete Brouwer function over grid [1 : n]d . Our bound is near...
Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivale...
Sergey Bravyi, Cristopher Moore, Alexander Russell
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...
The collision problem is to decide whether a function X : {1, . . . , n} {1, . . . , n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of...
— 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...