  We employ quantum-volume random-circuit sampling to benchmark the two-QPU
entanglement-assisted distributed quantum computing (DQC) and compare it with
single-QPU quantum computing. We first specify a single-qubit depolarizing
noise model in the random circuit. Based on this error model, we show the
one-to-one correspondence of three figures of merits, namely average gate
fidelity, heavy output probability, and linear cross-entropy. We derive an
analytical approximation of the average gate fidelity under the specified noise
model, which is shown to align with numerical simulations. The approximation is
calculated based on a noise propagation matrix obtained from the extended
connectivity graph of a DQC device. In numerical simulation, we unveil the
scalability enhancement in DQC for the QPUs with limited connectivity.
Furthermore, we provide a simple formula to estimate the average gate fidelity,
which also provides us with a heuristic method to evaluate the scalability
enhancement in DQC, and a guide to optimize the structure of a DQC
configuration.
