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arXiv:2103.16679 · npj Quantum Information

Hybrid light-matter networks of Majorana zero modes

Lauriane C. Contamin, Matthieu R. Delbecq, Benoît Douçot, Audrey Cottet, Takis Kontos

Published Dec 16, 2021• 27 citations
arXivHTMLPDF

Abstract

Abstract Topological excitations, such as Majorana zero modes, are a promising route for encoding quantum information. Topologically protected gates of Majorana qubits, based on their braiding, will require some form of network. Here, we propose to build such a network by entangling Majorana matter with light in a microwave cavity QED set-up. Our scheme exploits a light-induced interaction which is universal to all the Majorana nanoscale circuit platforms. This effect stems from a parametric drive of the light-matter coupling in a one-dimensional chain of physical Majorana modes. Our set-up enables all the basic operations needed in a Majorana quantum computing platform such as fusing, braiding, the crucial T-gate, the read-out, and importantly, the stabilization or correction of the physical Majorana modes.

DOI
10.1038/s41534-021-00508-w

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Abstract Topological excitations, such as Majorana zero modes, are a promising route for encoding quantum information. Topologically protected gates of Majorana qubits, based on their braiding, will require some form of network. Here, we propose to build such a network by entangling Majorana matter with light in a microwave cavity QED set-up. Our scheme exploits a light-induced interaction which is universal to all the Majorana nanoscale circuit platforms. This effect stems from a parametric drive of the light-matter coupling in a one-dimensional chain of physical Majorana modes. Our set-up enables all the basic operations needed in a Majorana quantum computing platform such as fusing, braiding, the crucial T-gate, the read-out, and importantly, the stabilization or correction of the physical Majorana modes.
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.
I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization and singular value decomposition of the Hamiltonian in the Majorana representation, while computing the mass gap of the MZM and its spectral properties. The interplay of cavity induced interactions and effective ppp-wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to a superradiant topological phase of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions that can be applied to other fermionic and analog systems termed Light-Matter-Majorana.
We propose and analyze a physical system capable of performing topological quantum computation with Majorana zero modes (MZMs) in a one-dimensional topological superconductor (1DTS). One of the leading methods to realize quantum gates in a 1DTS is to use T junctions, which allows one to maneuver MZMs in such a manner as to achieve braiding. In this paper, we propose a scheme for implementing quantum logical gates in a purely one-dimensional geometry without T junctions, instead replacing it with an auxiliary qubit. This has the additional benefit of introducing a non-Clifford gate, corresponding to one- and two-logical-qubit ZZZ rotations. We first design a topologically protected logical ZZZ gate based entirely on local interactions within the 1DTS. Using an auxiliary qubit coupled to the topological superconductors, we extend the ZZZ gate to non-Clifford single- and multiqubit arbitrary rotations with partial topological protection. Finally, to perform universal quantum computing, we introduce a scheme for performing arbitrary unitary rotations, albeit without topological protection. We develop a formalism based on unitary braids which creates transitions between different topological phases of the 1DTS system. The unitary formalism can be simply converted to an equivalent adiabatic scheme, which we numerically simulate, and we show that high-fidelity operations should be possible with reasonable parameters.
Abstract I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization with self-consistent order parameters and singular value decomposition of the Hamiltonian in the Majorana representation. I analyze the spectral properties of the system, the mass gap and amplitude of the MZM with a unified framework. The interplay of cavity induced interactions and effective p -wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to superradiant topological phases of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behavior of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions using Hartree–Fock–Bogoliubov theory in real space for finite systems that can be applied to other fermionic and analog systems termed Light-Matter-Majorana. A promising landscape for the exploration of short range and long range topological order with superradiance is found.
Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional systems, it has been shown that braiding can also be realized using one-dimensional wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and $\ensuremath{\pi}$, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the $\ensuremath{\pi}$ modes as auxiliary degrees of freedom.
Abstract We investigate the effects of coupling a local electromagnetic cavity to a segment of a topological Kitaev chain (KC), with particular emphasis on the interplay between photons and Majorana zero modes (MZMs). In addition to the well-known scissor effect-which effectively partitions the chain and isolates free MZMs in the bulk-we provide evidence of non-trivial fusion rules and braiding operations, hallmark signatures of non-Abelian anyons, enabled by spatially selective ultrastrong KC-cavity coupling. We propose that these distinctive MZM properties can be experimentally probed via fermionic parity measurements and photon-induced Berry phases. Furthermore, we demonstrate that, in the so-called sweet-spot regime, the coupled system can be mapped onto a Rabi-like model with a homodyne-rotated quadrature, offering a simplified yet powerful theoretical description. Exploiting the symmetry of fermionic modes within a two-site cavity configuration, we also show the feasibility of generating hybrid MZM-polariton Schrödinger cat states. Our findings offer a novel approach to manipulating topological quantum matter through local light–matter interactions and provide theoretical tools for future experimental realizations in platforms such as quantum materials or superconducting circuits.