Above: the statistical count (x) of the error signal (ptx) recorded by a single-load detector is shown by the number of repetitions

**A new methodology for the abstract and universal description of the fidelity of quantum circuits.**

Manipulating individual electrons for the purpose of using quantum effects offers new possibilities and greater accuracy in electronics. However, these single-electron circuits are governed by the laws of quantum mechanics, which means that deviations from error-free operation still occur (in the best possible scenario) very rarely. Therefore, perspectives on the physical origin and metrological aspects of this fundamental uncertainty are essential for further development of quantum circuits. To this end, scientists from the Physikalisch-Technische Bundesanstalt (PTB) and the University of Latvia have collaborated to develop a methodology for statistical analysis. Their results have been published in the journal Nature Communications.

Single-electron circuits are already used as a quantum standard for electric current and in prototypes of quantum computers. In these miniaturized quantum circuits, interactions and noise prevent the study of key uncertainties and measuring them is a challenge, as well as for the metrological accuracy of the measuring apparatus.

In the field of quantum computers, a test procedure called “reference” is often used, in which the principle of operation of the whole circuit and the fidelity are evaluated through an accumulation of errors after a sequence of operations. Based on this principle, researchers from PTB and the University of Latvia have developed a reference for single-electron circuits. Here, the fidelity of the circuit is described by the random steps of an error signal recorded by an integrated sensor while the circuit is repeatedly performing an operation. A statistical analysis of this “random walk” can be used to identify rare but unavoidable errors when manipulating individual quantum particles.

Through this “random walk reference”, the transfer of individual electrons was investigated in a single-electron pump circuit developed in PTB, the ampere, the SI basic unit, as the main standard for achievement. In this experiment, sensitive detectors record the error signal at a single electron resolution. Statistical analysis made possible by counting particular particles shows the basic limitations of circuit fidelity caused by external noise and time correlations, but also a strong measure of error assessment in applied quantum metrology.

The methodology developed in the framework of this work provides a rigorous mathematical basis for validating quantum standards for electrical quantities and opens up new avenues for the development of complex integrated quantum systems.

Reference: David Aifert, Martins Kokainis, Andris Ambainis, Vyacheslavs Kashcheyevs, and Niels Ubbelohde, “Random Route to Single-Electron Circuits,” January 12, 2021. *Nature Communications*.

DOI: 10.1038 / s41467-020-20554-w