Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits

Ezawa, Motohiko

doi:10.1103/physrevb.102.075424

Cited by 28 publications

(5 citation statements)

References 109 publications

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“…In what concerns the 2 n -root topological superconductor model introduced here, on the other hand, its direct implementation in a superconducting system seems out-of-reach with current technology, as it would require some very fine local tuning of the phases of the superconducting and hopping terms. Nevertheless, and as we explained in section V, one can simulate this model by translating it into its single-particle tight-binding analog model, which can be realized in the venues listed above or, as recently proposed, in topoelectrical circuits 46,47 .…”

Section: Discussionmentioning

confidence: 99%

One-dimensional $2^n$-root topological insulators and superconductors

Marques,

Madail,

Dias

2021

Preprint

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Square-root topology is a recently emerged sub-field describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to 2 n -root topological insulators and superconductors, with n any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of 2 n -root topological insulators/superconductors which connects the Hamiltonian of the starting model for any n, through a series of squaring operations followed by constant energy shifts, to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of 2 n -root topology to higher-dimensional systems.

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Section: Discussionmentioning

confidence: 99%

One-dimensional $2^n$-root topological insulators and superconductors

Marques,

Madail,

Dias

2021

Preprint

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“…where ω 0 is the free-running frequency of the oscillator, A i is the amplitude, and θ i is the phase. We now apply the results of [22], that were originally developed for LC resonators, to our oscillators. An N -qubit state is defined by the superposition of the 2 N states,…”

Section: B Proposed Approach: Polychronous Oscillatory Cnnmentioning

confidence: 99%

Quantum Computing Gate Emulation Using CMOS Oscillatory Cellular Neural Networks

Smith,

Lee

2024

IEEE Trans. Circuits Syst. II

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This paper presents quantum computing gate emulation using polychronous oscillatory cellular neural networks. The oscillatory neural network consists of locally interacting ring oscillators and control switches, in a standard CMOS process. We apply impulse sensitivity function (ISF) theory to model the injection locking of the oscillators. We show the design of universal quantum gate emulation with oscillator circuits. Quantum circuits for the Greenberger-Horne-Zeilinger State and W State are emulated using CMOS oscillators and switches. Spectre simulation results agree with the quantum circuit theory.

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“…In this work, we experimentally explore the QSSM by designing circuit networks. Recently, based on the similarity between circuit Laplacian and lattice Hamiltonian, simulating various physical phenomena with electric circuits has attracted lots of interest [21][22][23][24][25][26][27][28][29][30][31][32][33]. Compared with other classical platforms, circuit networks possess remarkable advantages of being versatile and reconfigurable.…”

Section: Introductionmentioning

confidence: 99%

Topolectrical circuit realization of quadrupolar surface semimetals

2022

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Recent studies have shown that there are two types of topological quadrupolar semimetals. One is the quadrupolar bulk semimetal, which is a conventional semimetal with gapless nodes in the bulk spectrum. The other type is named the quadrupolar surface semimetal, possessing a gapped bulk but gapless nodes on the surface spectrum. There have been many experiments on the implementation of quadrupolar bulk semimetals. However, the quadrupolar surface semimetal has never been realized. Here we report on the experimental realization of the quadrupolar surface semimetal in the circuit system. To highlight the properties of the quadrupolar surface semimetal, we also prepare a quadrupolar bulk semimetal in the circuit as a contrast. It has been demonstrated that the quadrupolar surface semimetal has a bulk band gap, but two gapless nodes appear on the surfaces. Also, the electrons not only concentrate on the hinges but also on the corresponding surfaces. Our studies provide novel ways to control electrical signals and may have potential applications in the field of intergraded circuit design.

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Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits

Cited by 28 publications

References 109 publications

One-dimensional $2^n$-root topological insulators and superconductors

One-dimensional $2^n$-root topological insulators and superconductors

Quantum Computing Gate Emulation Using CMOS Oscillatory Cellular Neural Networks

Topolectrical circuit realization of quadrupolar surface semimetals

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