Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a… Expand

A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time.Expand

A simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.Expand

An algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest is presented, and a new lower bound is proved showing that no algorithm can have sub linear dependence on tau.Expand

This work gives a new subexponential-time quantum algorithm for constructing nonzero isogenies between two such elliptic curves, assuming the Generalized Riemann Hypothesis (but with no other assumptions).Expand

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum… Expand

It is shown that quantum walk can be regarded as a universal computational primitive, with any quantum computation encoded in some graph, even if the Hamiltonian is restricted to be the adjacency matrix of a low-degree graph.Expand

The algorithm is based on a significantly improved simulation of the continuous- and fractional- query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error.Expand

The algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation, and allows the quantum phase estimation algorithm, whose dependence on $\epsilon$ is prohibitive, to be bypassed.Expand

A general definition of quantum random walks on graphs is discussed and with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog is illustrated.Expand