Benchmarking quantum processors with a single qubit

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 benchmark performance with respect to circuit depth. 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 depth 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.