# Benchmarking quantum processors with a single qubit

## TL;DR

This paper benchmarks IBM quantum processors using the DQC1 algorithm to evaluate performance and error sources, revealing circuit length and width as key factors affecting accuracy.

## Contribution

It introduces a benchmarking method for quantum processors using DQC1, analyzing how circuit parameters influence performance and error behavior.

## Key findings

- Circuit length is the main limiting factor for performance.
- Wider circuits perform better at the same gate count due to error randomization.
- Both random and systematic errors increase with circuit complexity.

## Abstract

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.