Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1407.2851 · Physica Scripta

Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator

Bernard van Heck, Timo Hyart, C. W. J. Beenakker

Published Aug 25, 2015• 11 citations
arXivHTMLPDF

Abstract

We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resonance frequency of the microwave cavity that encloses the Cooper pair box.

DOI
10.1088/0031-8949/2015/t164/014007

Related papers

Realization of superconducting transmon qubits based on topological insulator nanowires

Xiaopei Sun, Bing Li, Enna Zhuo +8 more

Topological-material-based Josephson junctions have the potential to be used to host Majorana zero modes and to construct topological qubits. For operating the topological qubits at an appropriate timescale to avoid decoherence and quasiparticle poisoning, one would eventually go to the time domain and embed the topological qubits into quantum electrodynamic circuits. Here, we constructed a topological-insulator-nanowire-based transmon qubit and demonstrated its strong coupling to a coplanar waveguide resonator. The flux-tunable spectrum and Rabi oscillations with a qubit lifetime T 1 of ∼ 0.5 μ s were observed. Such a hybrid platform, containing topological materials and quantum electrodynamic circuits, can further be used to study the physical properties such as Majorana zero modes in topological quantum circuits.

Applied Physics Letters•Apr 10, 2023•9 citations

Flux-controlled quantum computation with Majorana fermions

Timo Hyart, Bernard van Heck, Ion Cosma Fulga +3 more

Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization-braiding-measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory (RAMM), a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multiqubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.

arXiv:1303.4379•Physical Review B•Jul 17, 2013•344 citations

Majorana Qubit Rotations in Microwave Cavities

Thomas L. Schmidt, Andreas Nunnenkamp, Christoph Bruder

Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows us to perform arbitrary single-qubit operations.

arXiv:1211.2201•Physical Review Letters•Mar 6, 2013•52 citations

Four-Majorana qubit with charge readout: Dynamics and decoherence

Tommy Li, W. A. Coish, Michael Hell +2 more

We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.

arXiv:1807.05839•Physical review. B./Physical review. B•Nov 5, 2018•25 citations

The top-transmon: a hybrid superconducting qubit for parity-protected quantum computation

Fabian Hassler, Anton Akhmerov, C. W. J. Beenakker

Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform a quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system --- irrespective of any quasiparticle excitations. Here we propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. The advantage over an earlier proposal using a flux qubit is that the coupling can be switched on and off with exponential accuracy, promising a reduced sensitivity to charge noise.

arXiv:1105.0315•New Journal of Physics•Sep 9, 2011•152 citations

Proposal for Coherent Coupling of Majorana Zero Modes and Superconducting Qubits Using the 4π Josephson Effect

David Pekker, Chang-Yu Hou, Vladimir Manucharyan +1 more

We propose to use an ancilla fluxonium qubit to interact with a Majorana qubit hosted by a topological one-dimensional wire. The coupling is obtained using the Majorana qubit-controlled 4π Josephson effect to flux bias the fluxonium qubit. We demonstrate how this coupling can be used to sensitively identify topological superconductivity, to measure the state of the Majorana qubit, to construct 2-qubit operations, and to implement quantum memories with topological protection.

arXiv:1301.3161•Physical Review Letters•Sep 5, 2013•66 citations
We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resonance frequency of the microwave cavity that encloses the Cooper pair box.
Topological-material-based Josephson junctions have the potential to be used to host Majorana zero modes and to construct topological qubits. For operating the topological qubits at an appropriate timescale to avoid decoherence and quasiparticle poisoning, one would eventually go to the time domain and embed the topological qubits into quantum electrodynamic circuits. Here, we constructed a topological-insulator-nanowire-based transmon qubit and demonstrated its strong coupling to a coplanar waveguide resonator. The flux-tunable spectrum and Rabi oscillations with a qubit lifetime T 1 of ∼ 0.5 μ s were observed. Such a hybrid platform, containing topological materials and quantum electrodynamic circuits, can further be used to study the physical properties such as Majorana zero modes in topological quantum circuits.
Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization-braiding-measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory (RAMM), a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multiqubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.
Majorana bound states have been proposed as building blocks for qubits on which certain operations can be performed in a topologically protected way using braiding. However, the set of these protected operations is not sufficient to realize universal quantum computing. We show that the electric field in a microwave cavity can induce Rabi oscillations between adjacent Majorana bound states. These oscillations can be used to implement an additional single-qubit gate. Supplemented with one braiding operation, this gate allows us to perform arbitrary single-qubit operations.
We present a theoretical analysis of a Majorana-based qubit consisting of two topological superconducting islands connected via a Josephson junction. The qubit is operated by electrostatic gates which control the coupling of two of the four Majorana zero modes. At the end of the operation, readout is performed in the charge basis. Even though the operations are not topologically protected, the proposed experiment can potentially shed light on the coherence of the parity degree of freedom in Majorana devices and serve as a first step towards topological Majorana qubits. We discuss in detail the charge-stability diagram and its use for characterizing the parameters of the devices, including the overlap of the Majorana edge states. We describe the multilevel spectral properties of the system and present a detailed study of its controlled coherent oscillations, as well as decoherence resulting from coupling to a non-Markovian environment. In particular, we study a gate-controlled protocol where conversion between Coulomb-blockade and transmon regimes generates coherent oscillations of the qubit state due to the overlap of Majorana modes. We show that, in addition to fluctuations of the Majorana coupling, considerable measurement errors may be accumulated during the conversion intervals when electrostatic fluctuations in the superconducting islands are present. These results are also relevant for several proposed implementations of topological qubits which rely on readout based on charge detection.
Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform a quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system --- irrespective of any quasiparticle excitations. Here we propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. The advantage over an earlier proposal using a flux qubit is that the coupling can be switched on and off with exponential accuracy, promising a reduced sensitivity to charge noise.