• Open Access

Repetitive Quantum Nondemolition Measurement and Soft Decoding of a Silicon Spin Qubit

Xiao Xue, Benjamin D’Anjou, Thomas F. Watson, Daniel R. Ward, Donald E. Savage, Max G. Lagally, Mark Friesen, Susan N. Coppersmith, Mark A. Eriksson, William A. Coish, and Lieven M. K. Vandersypen
Phys. Rev. X 10, 021006 – Published 8 April 2020

Abstract

Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla. Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla. Repeating this procedure enhances the logical readout fidelity from 75.5±0.3% to 94.5±0.2% after 15 ancilla readouts. In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit. We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio. These results pave the way for the implementation of quantum error correction with spin qubits in silicon.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 29 November 2019
  • Accepted 3 March 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021006

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiao Xue1,‡, Benjamin D’Anjou2,‡, Thomas F. Watson1, Daniel R. Ward3, Donald E. Savage3, Max G. Lagally3, Mark Friesen3, Susan N. Coppersmith3,†, Mark A. Eriksson3, William A. Coish4, and Lieven M. K. Vandersypen1,*

  • 1QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands
  • 2Department of Physics, University of Konstanz, D-78457 Konstanz, Germany
  • 3University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
  • 4Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada

  • *Corresponding author. l.m.k.vandersypen@tudelft.nl
  • Present address: School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia.
  • These authors contributed equally to this work.

Popular Summary

For many quantum information processing tasks, including quantum error correction, it is important to measure a qubit state accurately while perturbing the qubit as little as allowed by quantum mechanics. This can be achieved by repeatedly mapping information from a data qubit to an ancilla qubit, each time followed by destructive measurement of the ancilla. The state of the data qubit is then inferred from the sequence of ancilla measurements. Here, we implement an ancilla-based repetitive readout of an electron-spin qubit and analyze its performance.

In ancilla-based information storage, there are two approaches to retrieving the data. In hard decoding, ancilla measurements are converted one by one to bit values, followed by a majority vote to determine the most likely state of the data qubit. This strategy may discard useful information. In soft decoding, the noisy signals from many ancilla measurements can be processed simultaneously. This strategy ideally extracts all available information in the measurements to optimally infer the state of the data qubit.

We encode quantum information in a single electron spin stored in one of two coupled quantum dots in silicon. A second electron spin, located in the other dot, acts as an ancilla qubit. We then measure and reinitialize the ancilla. After 15 repetitions, the measurement fidelity increases from 75.5% to 94.5%. Moreover, when Gaussian white noise dominates the overall measurement error, soft decoding is more efficient than hard decoding, thereby easing detector efficiency requirements for operation at a higher temperature and gate-based readout.

This work paves the way toward quantum error correction in silicon.

Key Image

Article Text

Click to Expand

References

Click to Expand
Issue

Vol. 10, Iss. 2 — April - June 2020

Subject Areas
Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review X

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×