  As we are entering the era of constructing practical quantum computers,
suppressing the inevitable noise to accomplish reliable computational tasks
will be the primary goal. Leakage noise, as the amplitude population leaking
outside the qubit subspace, is a particularly damaging source of error that
error correction approaches cannot handle. However, the impact of this noise on
the performance of variational quantum algorithms (VQAs), a type of near-term
quantum algorithms that is naturally resistant to a variety of noises, is yet
unknown. Here, {we consider a typical scenario with the widely used
hardware-efficient ansatz and the emergence of leakage in two-qubit gates},
observing that leakage noise generally reduces the expressive power of VQAs.
Furthermore, we benchmark the influence of leakage noise on VQAs in real-world
learning tasks. Results show that, both for data fitting and data
classification, leakage noise generally has a negative impact on the training
process and final outcomes. Our findings give strong evidence that VQAs are
vulnerable to leakage noise in most cases, implying that leakage noise must be
effectively suppressed in order to achieve practical quantum computing
applications, whether for near-term quantum algorithms and long-term
error-correcting quantum computing.
