Logo of the Physikalisch-Technische Bundesanstalt
symbolic picture: "magazines"

A benchmark for single-electron circuits

Methodology for a universal description of the accuracy of quantum circuits

PTBnews 3.2021
Especially interesting for


quantum information processing

electrical quantum metrology

Manipulating individual electrons with the goal of employing quantum effects promises qualitatively new applications in electronics. However, these single-electron circuits, which are governed by the laws of quantum mechanics, exhibit statistical deviations from error-free operation. This results in a fundamental uncertainty that is essential to understand and to quantify for further developments. To this end, PTB and the University of Latvia have collaborated to develop a statistical testing methodology.

Simulated developments of possible random-walk progressions of the error signal x across the number t of repetitions of the circuit operation, taking the counting statistics of the error signal that as measured experimentally into account. The orange curve emphasizes the example of one of these possible progressions. The linewidths of the blue curves correspond to the statistical frequencies of each of the assumed states.

Single-electron circuits are being developed as electric-current quantum standards and are already being used in quantum-computer prototypes. In these mesoscopic quantum circuits, interactions and noise-related processes impede the investigation of fundamental uncertainties. This therefore represents a considerable challenge for metrology at the highest level of precision.

In the field of quantum computers, a testing procedure is frequently used in which the operating principle and the accuracy of the entire circuit are evaluated via the accumulation of errors following a sequence of operations. Based on this, researchers from PTB and the University of Latvia have now developed a benchmark for single-electron circuits. Here, the circuit’s accuracy is described by the random steps of an error signal recorded by an integrated sensor while the circuit repeatedly executes an operation. The statistical analysis of this sequence, which is also called the “random walk”, can be used to identify the rare but unavoidable errors that occur when individual quantum particles are manipulated.

By means of this “random-walk benchmark”, the transfer of individual electrons was investigated in a circuit consisting of single-electron pumps. These single-electron pumps were developed at PTB as a primary standard for realizing the ampere, an SI base unit. In this experiment, sensitive charge detectors record the error signal with single-electron resolution. The statistical analysis made possible by counting individual particles not only shows fundamental limitations of the circuit’s accuracy induced by external noise and temporal correlations but also provides a robust measure of assessing errors in electrical quantum metrology.

The methodology developed within the scope of this work provides a rigorous mathematical foundation for validating quantum standards for electrical quantities and opens new paths for the development and analysis of the operating principle of complex quantum systems.


Niels Ubbelohde
Department 2.5
Semiconductor Physics and Magnetism
Phone: +49 531 592-2534
Opens local program for sending emailniels.ubbelohde(at)ptb.de

Scientific publication

D. Reifert, M. Kokainis, A. Ambainis, V. Kashcheyevs, N. Ubbelohde: A random-walk benchmark for single-electron circuits. Nat. Commun. 12, 285 (2021)
Opens external link in new windowhttps://doi.org/10.1038/s41467-020-20554-w