Interferometric single-shot parity measurement in InAs–Al hybrid devices

Morteza Aghaee, Alejandro Alcaraz Ramirez, Zulfi Alam, Rizwan Ali, Mariusz Andrzejczuk, Andrey Antipov, Mikhail Astafev, Amin Barzegar, Bela Bauer, Jonathan Becker, Umesh Kumar Bhaskar, Alex Bocharov, Srini Boddapati, David Bohn, Jouri Bommer, Leo Bourdet, Arnaud Bousquet, Samuel Boutin, Lucas Casparis, Benjamin J. Chapman, Sohail Chatoor, Anna Wulff Christensen, Cassandra Chua, Patrick Codd, William Cole, Paul Cooper, Fabiano Corsetti, Ajuan Cui, Paolo Dalpasso, Juan Pablo Dehollain, Gijs Lange, Michiel Moor, Andreas Ekefjärd, Tareq El Dandachi, Juan Carlos Estrada Saldaña, Saeed Fallahi, Luca Galletti, Geoff Gardner, Deshan Govender, Flavio Griggio, Ruben Grigoryan, Sebastian Grijalva, Sergei Gronin, Jan Gukelberger, Marzie Hamdast, Firas Hamze, Esben Bork Hansen, Sebastian Heedt, Zahra Heidarnia, Jesús Herranz Zamorano, Samantha Ho, Laurens Holgaard, John Hornibrook, Jinnapat Indrapiromkul, Henrik Ingerslev, Lovro Ivancevic, Thomas Jensen, Jaspreet Jhoja, Jeffrey Jones, Konstantin V. Kalashnikov, Ray Kallaher, Rachpon Kalra, Farhad Karimi, Torsten Karzig, Evelyn King, Maren Elisabeth Kloster, Christina Knapp, Dariusz Kocon, Jonne V. Koski, Pasi Kostamo, Mahesh Kumar, Tom Laeven, Thorvald Larsen, Jason Lee, Kyunghoon Lee, Grant Leum, Kongyi Li, Tyler Lindemann, Matthew Looij, Julie Love, Marijn Lucas, Roman Lutchyn, Morten Hannibal Madsen, Nash Madulid, Albert Malmros, Michael Manfra, Devashish Mantri, Signe Brynold Markussen, Esteban Martinez, Marco Mattila, Robert McNeil, Antonio B. Mei, Ryan V. Mishmash, Gopakumar Mohandas, Christian Mollgaard, Trevor Morgan, George Moussa, Chetan Nayak (), Jens Hedegaard Nielsen, Jens Munk Nielsen, William Hvidtfelt Padkar Nielsen, Bas Nijholt, Mike Nystrom, Eoin O’Farrell, Thomas Ohki, Keita Otani, Brian Paquelet Wütz, Sebastian Pauka, Karl Petersson, Luca Petit, Dima Pikulin, Guen Prawiroatmodjo, Frank Preiss, Eduardo Puchol Morejon, Mohana Rajpalke, Craig Ranta, Katrine Rasmussen, David Razmadze, Outi Reentila, David J. Reilly, Yuan Ren, Ken Reneris, Richard Rouse, Ivan Sadovskyy, Lauri Sainiemi, Irene Sanlorenzo, Emma Schmidgall, Cristina Sfiligoj, Mustafeez Bashir Shah, Kevin Simoes, Shilpi Singh, Sarat Sinha, Thomas Soerensen, Patrick Sohr, Tomas Stankevic, Lieuwe Stek, Eric Stuppard, Henri Suominen, Judith Suter, Sam Teicher, Nivetha Thiyagarajah, Raj Tholapi, Mason Thomas, Emily Toomey, Josh Tracy, Michelle Turley, Shivendra Upadhyay, Ivan Urban, Kevin Hoogdalem, David J. Woerkom, Dmitrii V. Viazmitinov, Dominik Vogel, John Watson, Alex Webster, Joseph Weston, Georg W. Winkler, Di Xu, Chung Kai Yang, Emrah Yucelen, Roland Zeisel, Guoji Zheng and Justin Zilke
Additional contact information
Morteza Aghaee: Microsoft Azure Quantum
Alejandro Alcaraz Ramirez: Microsoft Azure Quantum
Zulfi Alam: Microsoft Azure Quantum
Rizwan Ali: Microsoft Azure Quantum
Mariusz Andrzejczuk: Microsoft Azure Quantum
Andrey Antipov: Microsoft Azure Quantum
Mikhail Astafev: Microsoft Azure Quantum
Amin Barzegar: Microsoft Azure Quantum
Bela Bauer: Microsoft Azure Quantum
Jonathan Becker: Microsoft Azure Quantum
Umesh Kumar Bhaskar: Microsoft Azure Quantum
Alex Bocharov: Microsoft Azure Quantum
Srini Boddapati: Microsoft Azure Quantum
David Bohn: Microsoft Azure Quantum
Jouri Bommer: Microsoft Azure Quantum
Leo Bourdet: Microsoft Azure Quantum
Arnaud Bousquet: Microsoft Azure Quantum
Samuel Boutin: Microsoft Azure Quantum
Lucas Casparis: Microsoft Azure Quantum
Benjamin J. Chapman: Microsoft Azure Quantum
Sohail Chatoor: Microsoft Azure Quantum
Anna Wulff Christensen: Microsoft Azure Quantum
Cassandra Chua: Microsoft Azure Quantum
Patrick Codd: Microsoft Azure Quantum
William Cole: Microsoft Azure Quantum
Paul Cooper: Microsoft Azure Quantum
Fabiano Corsetti: Microsoft Azure Quantum
Ajuan Cui: Microsoft Azure Quantum
Paolo Dalpasso: Microsoft Azure Quantum
Juan Pablo Dehollain: Microsoft Azure Quantum
Gijs Lange: Microsoft Azure Quantum
Michiel Moor: Microsoft Azure Quantum
Andreas Ekefjärd: Microsoft Azure Quantum
Tareq El Dandachi: Microsoft Azure Quantum
Juan Carlos Estrada Saldaña: Microsoft Azure Quantum
Saeed Fallahi: Microsoft Azure Quantum
Luca Galletti: Microsoft Azure Quantum
Geoff Gardner: Microsoft Azure Quantum
Deshan Govender: Microsoft Azure Quantum
Flavio Griggio: Microsoft Azure Quantum
Ruben Grigoryan: Microsoft Azure Quantum
Sebastian Grijalva: Microsoft Azure Quantum
Sergei Gronin: Microsoft Azure Quantum
Jan Gukelberger: Microsoft Azure Quantum
Marzie Hamdast: Microsoft Azure Quantum
Firas Hamze: Microsoft Azure Quantum
Esben Bork Hansen: Microsoft Azure Quantum
Sebastian Heedt: Microsoft Azure Quantum
Zahra Heidarnia: Microsoft Azure Quantum
Jesús Herranz Zamorano: Microsoft Azure Quantum
Samantha Ho: Microsoft Azure Quantum
Laurens Holgaard: Microsoft Azure Quantum
John Hornibrook: Microsoft Azure Quantum
Jinnapat Indrapiromkul: Microsoft Azure Quantum
Henrik Ingerslev: Microsoft Azure Quantum
Lovro Ivancevic: Microsoft Azure Quantum
Thomas Jensen: Microsoft Azure Quantum
Jaspreet Jhoja: Microsoft Azure Quantum
Jeffrey Jones: Microsoft Azure Quantum
Konstantin V. Kalashnikov: Microsoft Azure Quantum
Ray Kallaher: Microsoft Azure Quantum
Rachpon Kalra: Microsoft Azure Quantum
Farhad Karimi: Microsoft Azure Quantum
Torsten Karzig: Microsoft Azure Quantum
Evelyn King: Microsoft Azure Quantum
Maren Elisabeth Kloster: Microsoft Azure Quantum
Christina Knapp: Microsoft Azure Quantum
Dariusz Kocon: Microsoft Azure Quantum
Jonne V. Koski: Microsoft Azure Quantum
Pasi Kostamo: Microsoft Azure Quantum
Mahesh Kumar: Microsoft Azure Quantum
Tom Laeven: Microsoft Azure Quantum
Thorvald Larsen: Microsoft Azure Quantum
Jason Lee: Microsoft Azure Quantum
Kyunghoon Lee: Microsoft Azure Quantum
Grant Leum: Microsoft Azure Quantum
Kongyi Li: Microsoft Azure Quantum
Tyler Lindemann: Microsoft Azure Quantum
Matthew Looij: Microsoft Azure Quantum
Julie Love: Microsoft Azure Quantum
Marijn Lucas: Microsoft Azure Quantum
Roman Lutchyn: Microsoft Azure Quantum
Morten Hannibal Madsen: Microsoft Azure Quantum
Nash Madulid: Microsoft Azure Quantum
Albert Malmros: Microsoft Azure Quantum
Michael Manfra: Microsoft Azure Quantum
Devashish Mantri: Microsoft Azure Quantum
Signe Brynold Markussen: Microsoft Azure Quantum
Esteban Martinez: Microsoft Azure Quantum
Marco Mattila: Microsoft Azure Quantum
Robert McNeil: Microsoft Azure Quantum
Antonio B. Mei: Microsoft Azure Quantum
Ryan V. Mishmash: Microsoft Azure Quantum
Gopakumar Mohandas: Microsoft Azure Quantum
Christian Mollgaard: Microsoft Azure Quantum
Trevor Morgan: Microsoft Azure Quantum
George Moussa: Microsoft Azure Quantum
Chetan Nayak: Microsoft Azure Quantum
Jens Hedegaard Nielsen: Microsoft Azure Quantum
Jens Munk Nielsen: Microsoft Azure Quantum
William Hvidtfelt Padkar Nielsen: Microsoft Azure Quantum
Bas Nijholt: Microsoft Azure Quantum
Mike Nystrom: Microsoft Azure Quantum
Eoin O’Farrell: Microsoft Azure Quantum
Thomas Ohki: Microsoft Azure Quantum
Keita Otani: Microsoft Azure Quantum
Brian Paquelet Wütz: Microsoft Azure Quantum
Sebastian Pauka: Microsoft Azure Quantum
Karl Petersson: Microsoft Azure Quantum
Luca Petit: Microsoft Azure Quantum
Dima Pikulin: Microsoft Azure Quantum
Guen Prawiroatmodjo: Microsoft Azure Quantum
Frank Preiss: Microsoft Azure Quantum
Eduardo Puchol Morejon: Microsoft Azure Quantum
Mohana Rajpalke: Microsoft Azure Quantum
Craig Ranta: Microsoft Azure Quantum
Katrine Rasmussen: Microsoft Azure Quantum
David Razmadze: Microsoft Azure Quantum
Outi Reentila: Microsoft Azure Quantum
David J. Reilly: Microsoft Azure Quantum
Yuan Ren: Microsoft Azure Quantum
Ken Reneris: Microsoft Azure Quantum
Richard Rouse: Microsoft Azure Quantum
Ivan Sadovskyy: Microsoft Azure Quantum
Lauri Sainiemi: Microsoft Azure Quantum
Irene Sanlorenzo: Microsoft Azure Quantum
Emma Schmidgall: Microsoft Azure Quantum
Cristina Sfiligoj: Microsoft Azure Quantum
Mustafeez Bashir Shah: Microsoft Azure Quantum
Kevin Simoes: Microsoft Azure Quantum
Shilpi Singh: Microsoft Azure Quantum
Sarat Sinha: Microsoft Azure Quantum
Thomas Soerensen: Microsoft Azure Quantum
Patrick Sohr: Microsoft Azure Quantum
Tomas Stankevic: Microsoft Azure Quantum
Lieuwe Stek: Microsoft Azure Quantum
Eric Stuppard: Microsoft Azure Quantum
Henri Suominen: Microsoft Azure Quantum
Judith Suter: Microsoft Azure Quantum
Sam Teicher: Microsoft Azure Quantum
Nivetha Thiyagarajah: Microsoft Azure Quantum
Raj Tholapi: Microsoft Azure Quantum
Mason Thomas: Microsoft Azure Quantum
Emily Toomey: Microsoft Azure Quantum
Josh Tracy: Microsoft Azure Quantum
Michelle Turley: Microsoft Azure Quantum
Shivendra Upadhyay: Microsoft Azure Quantum
Ivan Urban: Microsoft Azure Quantum
Kevin Hoogdalem: Microsoft Azure Quantum
David J. Woerkom: Microsoft Azure Quantum
Dmitrii V. Viazmitinov: Microsoft Azure Quantum
Dominik Vogel: Microsoft Azure Quantum
John Watson: Microsoft Azure Quantum
Alex Webster: Microsoft Azure Quantum
Joseph Weston: Microsoft Azure Quantum
Georg W. Winkler: Microsoft Azure Quantum
Di Xu: Microsoft Azure Quantum
Chung Kai Yang: Microsoft Azure Quantum
Emrah Yucelen: Microsoft Azure Quantum
Roland Zeisel: Microsoft Azure Quantum
Guoji Zheng: Microsoft Azure Quantum
Justin Zilke: Microsoft Azure Quantum

Nature, 2025, vol. 638, issue 8051, 651-655

Abstract: Abstract The fusion of non-Abelian anyons is a fundamental operation in measurement-only topological quantum computation1. In one-dimensional topological superconductors (1DTSs)2–4, fusion amounts to a determination of the shared fermion parity of Majorana zero modes (MZMs). Here we introduce a device architecture5 that is compatible with future tests of fusion rules. We implement a single-shot interferometric measurement of fermion parity6–11 in indium arsenide–aluminium heterostructures with a gate-defined superconducting nanowire12–14. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of the quantum capacitance of these quantum dots of up to 1 fF. Our quantum-capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio (SNR) of 1 in 3.6 μs at optimal flux values. From the time traces of the quantum-capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. We discuss the interpretation of our measurements in terms of both topologically trivial and non-trivial origins. The large capacitance shift and long poisoning time enable a parity measurement with an assignment error probability of 1%.

Date: 2025
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DOI: 10.1038/s41586-024-08445-2

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