… , a quantum computer can naturally represent those amplitudes using only n quantum bits.
Thus… used to demonstrate exponential speedup of quantum over classical computation Childs …

In some of the earliest work on quantum computing, Feynman showed how to implement
universal quantum computation with a time-independent Hamiltonian. I show that this remains …

… We define this formally for trees T in which each internal vertex has two children (it will
not be necessary to consider others). A random embedding is obtained as follows: …

Background A study conducted in 1983 to identify and rank the symptoms experienced by
patients receiving cancer chemotherapy reported that vomiting and nausea were the most …

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 …

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum
computer by approximating the truncated Taylor series of the evolution operator. Our method …

Harrow, Hassidim, and Lloyd [Phys. Rev. Lett., 103 (2009), 150502] showed that for a suitably
specified $N \times N$ matrix $A$ and an $N$-dimensional vector $\vec{b}$, there is a …

In this note, we discuss a general definition of quantum random walks on graphs and illustrate
with a simple graph the possibility of very different behavior between a classical random …

We study the fault tolerance of quantum computation by adiabatic evolution, a quantum
algorithm for solving various combinatorial search problems. We describe an inherent …

… However, I am not aware of an efficient algorithm to compute even a single nontrivial bit
of information about the Kloosterman sum, such as its sign or whether its magnitude is larger …