  Neutral atom quantum processors provide a viable route to scalable quantum
computing, with recent demonstrations of high-fidelity and parallel gate
operations and initial implementation of quantum algorithms using both physical
and logical qubit encodings. In this work we present a characterization of the
algorithmic performance of near term Rydberg atom quantum computers through
device simulation to enable comparison against competing architectures. We
consider three different quantum algorithm related tests, exploiting the
ability to dynamically update qubit connectivity and multi-qubit gates. We
calculate a quantum volume of $\mathbf{\mathit{V_{Q}}=2^{9}}$ for 9 qubit
devices with realistic parameters, which is the maximum achievable value for
this device size and establishes a lower bound for larger systems. We also
simulate highly efficient implementations of both the Bernstein-Vazirani
algorithm with >0.95 success probability for 9 data qubits and 1 ancilla qubit
without loss correction, and Grover's search algorithm with a loss-corrected
success probability of 0.97 for an implementation of the algorithm using 6 data
qubits and 3 ancilla qubits using native multi-qubit $\mathbf{CCZ}$ gates. Our
results indicate Rydberg atom processors are a highly competitive near-term
platform which, bolstered by the potential for further scalability, can pave
the way toward useful quantum computation.
