  The first generation of small noisy quantum processors have recently become
available to non-specialists who are not required to understand specifics of
the physical platforms and, in particular, the types and sources of noise. As
such, it is useful to benchmark the performance of such computers against
specific tasks that may be of interest to users, ideally keeping both the
circuit depth and width as free parameters. Here we benchmark the IBM Quantum
Experience using the Deterministic Quantum Computing with 1 qubit (DQC1)
algorithm originally proposed by Knill and Laflamme in the context of liquid
state NMR. In the first set of experiments we use DQC1 as a trace estimation
algorithm to produce visibility plots. In the second set we use this trace
estimation algorithm to distinguish between knots, a classically difficult task
which is known to be complete for DQC1. Our results indicate that the main
limiting factor is the length of the circuit, and that both random and
systematic errors become an issue when the gate count increases. Surprisingly,
we find that at the same gate count wider circuits perform better, probably due
to randomization of coherent errors.
