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Nature

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

Microsoft Azure Quantum, Morteza Aghaee, Alejandro Alcaraz Ramirez, Zulfi Alam, Rizwan Ali, Mariusz Andrzejczuk, Andrey E. Antipov, Mikhail A. Astafev, Amin Barzegar, Bela Bauer, Jonathan Becker, Umesh Kumar Bhaskar, Alex Bocharov, Srini Boddapati, David Bohn, Jouri D. S. Bommer, L. Bourdet, A. Bousquet, Samuel Boutin, Lucas Casparis, Benjamin J. Chapman, Sohail Chatoor, Anna Wulff Christensen, Cassandra Chua, Patrick Codd, William S. Cole, Paul Cooper, Fabiano Corsetti, Ajuan Cui, Paolo Dalpasso, Juan Pablo Dehollain, G. de Lange, Michiel W. A. de Moor, Andreas Ekefjärd, Tareq El Dandachi, Juan Carlos Estrada Saldaña, Saeed Fallahi, Luca Galletti, G. C. Gardner, Deshan Govender, Flavio Griggio, Ruben Grigoryan, Sebastián Grijalva, Sergei Gronin, Jan Gukelberger, Marzie Hamdast, Firas Hamze, Esben Bork Hansen, Sebastian Heedt, Zahra Heidarnia, Jesús Herranz Zamorano, Samantha Ho, Laurens Holgaard, J. M. Hornibrook, Jinnapat Indrapiromkul, Henrik Ingerslev, Lovro Ivancevic, Thomas Jensen, Jaspreet Jhoja, Jeffrey Jones, K. V. Kalashnikov, Ray Kallaher, Rachpon Kalra, Farhad Karimi, Torsten Karzig, Cameron King, Maren Elisabeth Kloster, Christina Knapp, Dariusz Kocoń, Jonne Koski, Pasi Kostamo, Mahesh Kumar, Tom Laeven, T. W. Larsen, Jason Lee, Kyunghoon Lee, Grant Leum, Kongyi Li, Tyler Lindemann, Matthew Looij, Julie Love, Marijn Lucas, Roman M. Lutchyn, Morten Hannibal Madsen, Nash Madulid, Albert Malmros, Michael J. Manfra, Devashish Mantri, Signe Brynold Markussen, Esteban Martínez, Marco Mattila, Robert McNeil, Antonio B. Mei, Ryan V. Mishmash, Gopakumar Mohandas, Christian Mollgaard, Trevor Morgan, George Moussa, Chetan Nayak, Jens Hedegaard Nielsen

Published Feb 19, 2025• 158 citations
Publisher

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%. A device architecture based on indium arsenide–aluminium heterostructures with a gate-defined superconducting nanowire allows single-shot interferometric measurement of fermion parity and demonstrates an assignment error probability of 1%.

DOI
10.1038/s41586-024-08445-2

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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%. A device architecture based on indium arsenide–aluminium heterostructures with a gate-defined superconducting nanowire allows single-shot interferometric measurement of fermion parity and demonstrates an assignment error probability of 1%.
A central promise of topological quantum computing is that increasing the excitation gap improves device performance significantly. Here, we experimentally validate this principle in an InAs--Pb tetron device via interferometric single-shot parity measurements. By replacing aluminum with the higher-gap superconductor lead in our superconductor-semiconductor hybrid devices, we have improved the robustness of our topological phase. In addition, to enable fast and precise bring-up at scale, we have developed an rf measurement technique that resolves low-energy wire-end states and directly measures their energy splitting with μeVμ\text{eV}μeV precision. We employ this technique to bring up a device in a multi-tetron array and perform parity measurements of one of the tetron's hybrid nanowires (NWs). By controllably switching the wire parity, we observe h/2eh/2eh/2e-periodic bimodal shifts in the quantum capacitance of a quantum dot coupled to the hybrid nanowire in an interference loop. Further time-resolved measurements reveal a characteristic parity switching time of ∼20\sim 20∼20 s with some instances reaching minute-scale. Such extremely long parity lifetimes are orders of magnitude longer than typical qubit operation times, which are on the order of μsμ\text{s}μs. Finally, we discuss potential implications for the fidelity of Pauli measurements.
In a recent breakthrough experiment [Nature (London) 614, 445 (2023)], signatures of Majorana zero modes have been observed in tunnel spectroscopy for a minimal Kitaev chain constructed from coupled quantum dots. However, as Ising anyons, Majoranas' most fundamental property of non-Abelian statistics is yet to be detected. Moreover, the minimal Kitaev chain is qualitatively different from topological superconductors in that it supports Majoranas only at a sweet spot. Therefore, it is not obvious whether non-Abelian characteristics such as braiding and fusion can be demonstrated in this platform with a reasonable level of robustness. In this work, we theoretically propose a protocol for detecting the Majorana fusion rules in an artificial Kitaev chain consisting of four quantum dots. In contrast with the previous proposals for semiconductor-superconductor hybrid nanowire platforms, here we do not rely on mesoscopic superconducting islands, which are difficult to implement in quantum dot chains. To show the robustness of the fusion protocol, we discuss the effects of three types of realistic imperfections on the fusion outcomes, e.g., diabatic errors, dephasing errors, and calibration errors. We also propose a fermion parity readout scheme using quantum capacitance. Our work will shed light on future experiments on detecting the non-Abelian properties of Majorana modes in a quantum dot chain.
Quantum computers can solve some problems exponentially faster than classical computers. Unfortunately, the computational power of quantum computers is currently limited by the number of working qubits. It is difficult to scale up these systems, because qubits are easily affected by noise in their environment. This noise leads to decoherence: loss of the qubit’s encoded information. A possible solution to diminish decoherence is using Majorana box qubits, as these qubits are predicted to be insensitive to local noise. However, this promising type of qubit does not exist yet. With the research described in this thesis, we aim to contribute to the development of Majorana box qubits (MBQs). In these qubits, Majorana zero modes, the basic elements of MBQs, are contained within a superconducting island to suppress Majorana parity fluctuations caused by quasiparticle poisoning. To enable parity readout of the MBQ, these modes are coupled to quantum dots within a nanowire network. To help realize MBQs, we need a better understanding of quasiparticles in superconducting islands, parity-readout techniques, and ways to fabricate nanowire networks. These three aspects are the focus of the experiments presented in this thesis. To study superconducting islands and readout techniques, we used InAs semiconductor nanowires with an epitaxially grown Al shell. Majorana signatures have already been observed in such nanowires. We addressed quasiparticle dynamics in superconducting islands by measuring the gate-charge modulation of the switching current. We found a consistent 2e-periodic modulation at zero magnetic field, and an exponential decrease of parity lifetime with increasing magnetic field. We explored MBQ readout, using a quantum dot level as a proxy for a Majorana zero mode, and measured its charge hybridization with another dot using gate-based readout. We showed that we can rapidly discriminate between two settings with different tunnel couplings, demonstrating the potential of gate-based readout to measure MBQs. And, using gate-based readout, we could study charge-transfer processes occurring in hybrid structures of superconducting islands coupled to quantum dots. Finally, to find a good material platform for nanowire networks, we characterized two two-dimensional systems. We realized quantum point contacts in InSb, which we used to measure the ggg-factor anisotropy, and effective electron mass in this system. And, we studied the spin-orbit interaction in InAs/GaSb by extracting the difference in density between electrons with different spin orientations. This thesis finishes with a proposal for a series experiments to realize MBQs. These experiments make use of superconducting islands and the reflectometry setup we developed for gate-based readout.
The modern understanding of the Josephson effect in mesosopic devices derives from the physics of Andreev bound states, fermionic modes that are localized in a superconducting weak link. Recently, Josephson junctions constructed using semiconducting nanowires have led to the realization of superconducting qubits with gate-tunable Josephson energies. We have used a microwave circuit QED architecture to detect Andreev bound states in such a gate-tunable junction based on an aluminum-proximitized indium arsenide nanowire. We demonstrate coherent manipulation of these bound states, and track the bound-state fermion parity in real time. Individual parity-switching events due to nonequilibrium quasiparticles are observed with a characteristic timescale T_{parity}=160±10 μs. The T_{parity} of a topological nanowire junction sets a lower bound on the bandwidth required for control of Majorana bound states.
Dispersive charge sensing is realized in hybrid semiconductor-superconductor nanowires in gate-defined single- and double-island device geometries. Signal-to-noise ratios (SNRs) were measured in both the frequency and time domains. Frequency-domain measurements were carried out as a function of frequency and power and yield a charge sensitivity of 1 × 10–3 e/Hz for an ∼11 MHz measurement bandwidth. Time-domain measurements yield SNR > 1 for a 20 μs integration time. At zero magnetic field, photon-assisted tunneling was detected dispersively in a double-island geometry, indicating coherent hybridization of the two superconducting islands. At an axial magnetic field of 0.6 T, subgap states are detected dispersively, demonstrating the suitability of the method to sensing in the topological regime.
Recent experiments have measured flux dependent capacitance at radio frequencies leading to the potential for a fast parity read-out of a Majorana qubit. In this work we argue that the quantum dot used in the capacitance measurement can be reasonably approximated by a non-interacting weakly coupled orbital. We then predict the measured flux and parity dependent capacitance for several parameter regimes of the disordered Majorana nanowire model that are both topological and trivial. Following this we study how such a fast capacitance read-out can be used to characterize the quantum coherence of a Majorana nanowire-based qubit using Rabi oscillations. We additionally show that such measurements, if made possible by coherent inter-wire tunneling, would provide a valuable way of characterizing the low energy states in the frequency domain.