# All

## Vertices cannot be hidden from quantum spatial search for almost all random graphs. (arXiv:1709.06829v1 [quant-ph])

In this paper we show that all nodes can be found optimally for almost all
random Erd\H{o}s-R\'enyi ${\mathcal G}(n,p)$ graphs using continuous-time
quantum spatial search procedure. This works for both adjacency and Laplacian
matrices, though under different conditions. The first one requires
$p=\omega(\log^8(n)/n)$, while the seconds requires $p\geq(1+\varepsilon)\log (n)/n$, where $\varepsilon>0$. The proof was made by analyzing the convergence

## Halving the cost of quantum addition. (arXiv:1709.06648v1 [quant-ph])

We improve the number of T gates needed to perform an n-bit adder from 8n +
O(1) to 4n + O(1). We do so via a "temporary logical-AND" construction, which
uses four T gates to store the logical-AND of two qubits into an ancilla and
zero T gates to later erase the ancilla. Temporary logical-ANDs are a generally
useful tool when optimizing T-counts. They can be applied to integer
arithmetic, modular arithmetic, rotation synthesis, the quantum Fourier
transform, Shor's algorithm, Grover oracles, and many other circuits. Because T