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:2401.01703

Proposal of detecting topological transition of quantum braiding in three-fold degenerate eigen subspace

Zhi-Wei Han, Jia-Hao Liang, Zhao-Xin Fu, Hongzhi Liu, Ziyuan Chen, Meng Wang, Ze-Rui He, Huang, Jia-Yi, Qing-Xian Lv, Kai-Yu Liao, Yan-Xiong Du

Published Jan 3, 2024• 0 citations
arXivHTMLPDF

Abstract

The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once that the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally-feasible system provides a platform to investigate braiding dynamics, the SU(3) physics and the qutrit gates.

DOI
10.48550/arxiv.2401.01703

Related papers

Detecting a topological transition of quantum braiding in a threefold-degenerate eigensubspace

Zhi-Wei Han, Jia-Hao Liang, Zhao-Xin Fu +8 more

The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a threefold-degenerate eigensubspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally feasible system provides a platform to investigate braiding dynamics, the SU(3) physics, and the qutrit gates.

Physical Review A•Feb 22, 2024•2 citations

Majorana zero modes in multiplicative topological phases

Adipta Pal, Joe H. Winter, Ashley M. Cook

Topological qubits composed of unpaired Majorana zero modes are under intense experimental and theoretical scrutiny in efforts to realize practical quantum computation schemes. In this work, we show that the minimum four Majorana zero modes required for a topological qubit according to braiding schemes and control of entanglement for gate operations are inherent to multiplicative topological phases, which realize symmetry-protected tensor products—and maximally entangled Bell states—of unpaired Majorana zero modes. We construct and characterize both one-dimensional and two-dimensional multiplicative topological phases with two parent Kitaev chain Hamiltonians. We furthermore characterize topology in the bulk and on the boundary with established methods while also introducing techniques to overcome challenges in characterizing multiplicative topology. In the process, we explore the potential of these multiplicative topological phases for an alternative to braiding-based topological quantum computation schemes, in which gate operations are performed through topological phase transitions. Published by the American Physical Society 2024

arXiv:2301.02765•Physical review. B./Physical review. B•Jan 18, 2024•8 citations

Experimental topological quantum computing with electric circuits

Deyuan Zou, Naiqiao Pan, Tian Chen +2 more

The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches to solving these problems. Various theoretical schemes for building topological quantum computation have been proposed. However, experimental implementation has always been a great challenge because it has proved to be extremely difficult to create and manipulate topological qubits in real systems. Therefore, topological quantum computation has not been realized in experiments yet. Here, we report the first experimental realization of topological quantum computation with electric circuits. Based on our proposed new scheme with circuits, Majorana-like edge states are not only observed experimentally, but also T junctions are constructed for the braiding process. Furthermore, we demonstrate the feasibility of topological quantum computing through a set of one- and two-qubit unitary operations. Finally, our implementation of Grover's search algorithm demonstrates that topological quantum computation is ideally suited for such tasks.

arXiv:2309.04896•Sep 9, 2023•0 citations

Paper XXVI: Quantum Computation from Hopf Solitons — Topological Confinement of a Singlet–Triplet Orientation Qubit

Alexander Novickis

Abstract We propose the Hopf soliton vacuum --- the topological field-theoretic framework of Papers I--XV --- as a 3+1-dimensional platform for topological quantum computation (TQC). A qubit is encoded in the mutual linking number $L \in \{0, 1\}$ of a Hopf soliton pair: $|0\rangle$ corresponds to an unlinked pair, $|1\rangle$ to a linked pair. Since linking number is an integer topological invariant, the qubit is passively protected against decoherence --- errors require reconnection events exponentially suppressed at energies below the soliton mass gap $\Delta$. The SU(2)$_1$ Chern-Simons theory governing the Hopf vacuum (Paper V) provides the R-matrix $R = e^{i\pi/4}$ for soliton exchange, yielding Abelian (semionic) braiding. While SU(2)$_1$ alone is not universal, the 3+1D loop braid group provides additional operations (leapfrogging) beyond 2+1D braiding, and universality can be achieved via magic state distillation. We construct a gate set from soliton self-linking (single-qubit rotations) and inter-pair braiding (entangling gates), showing that topological protection yields error rates exponentially small in the ratio of system size to correlation length. Physical implementations include liquid crystal Hopfions, BEC vortex knots, and photonic topological states. This is a theoretical proposal: no experimental realization currently exists. > [!warning] Speculative Content > This paper is a theoretical proposal. The identification of Hopf soliton pairs as a TQC platform is new and untested. Standard TQC theory (Kitaev, Freedman et al., Nayak et al.) is well-established; the application to Hopf solitons is speculative. We clearly distinguish established results from proposals throughout. Keywords physics quantum computing topology anyons braiding TQC hopf solitons Type Preprint License CC BY 4.0 Date 2026-03-22 Subject Theoretical Physics DOI 10.5281/zenodo.19108219 © 2026 Alexander Novickis. Licensed under Creative Commons Attribution 4.0 International.

•Mar 19, 2026•0 citations

Many-Body Majorana Braiding without an Exponential Hilbert Space

Eric Mascot, Themba Hodge, Daniel Crawford +3 more

Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.

arXiv:2303.00761•Physical Review Letters•Oct 24, 2023•21 citations

Braided Majorana qubits as a minimal ingredient for Topological Quantum Computation?

Francesco Toppan

I point out that a possible minimal setting to realize Kitaev's proposal of a Topological Quantum Computation which offers topological protection from decoherence could in principle be realized by braided Majorana qubits. Majorana qubits and their braiding were introduced in Nucl. Phys. B 980, 115834 (2022) and further analyzed in J. Phys. A: Math. Theor. 57, 435203 (2024). Braided Majorana qubits implement a Gentile-type parastatistics with at most s-1 excited states accommodated in a multiparticle sector (the integer s=2,3,4,... labels quantum group reps at roots of unity). It is argued that braided Majorana qubits could play, for topological quantum computers, the same role as standard bits for ordinary computers and as qubits for "ordinary" quantum computers.

arXiv:2504.02125•Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)•Dec 9, 2025•1 citation
The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once that the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally-feasible system provides a platform to investigate braiding dynamics, the SU(3) physics and the qutrit gates.
The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a threefold-degenerate eigensubspace can be obtained in a four-level Hamiltonian which is the minimal physical system. Braiding operations are proposed to apply to dressed states in the subspace. The topology of the braiding diagram can be characterized through physical methods once the sequential braiding pulses are adopted. We establish an equivalent relationship function between the permutation group and the output states where different output states correspond to different values of the function. The topological transition of the braiding happens when two operations overlap, which is detectable through the measurement of the function. Combined with the phase variation method, we can analyze the wringing pattern of the braiding. Therefore, the experimentally feasible system provides a platform to investigate braiding dynamics, the SU(3) physics, and the qutrit gates.
Topological qubits composed of unpaired Majorana zero modes are under intense experimental and theoretical scrutiny in efforts to realize practical quantum computation schemes. In this work, we show that the minimum four Majorana zero modes required for a topological qubit according to braiding schemes and control of entanglement for gate operations are inherent to multiplicative topological phases, which realize symmetry-protected tensor products—and maximally entangled Bell states—of unpaired Majorana zero modes. We construct and characterize both one-dimensional and two-dimensional multiplicative topological phases with two parent Kitaev chain Hamiltonians. We furthermore characterize topology in the bulk and on the boundary with established methods while also introducing techniques to overcome challenges in characterizing multiplicative topology. In the process, we explore the potential of these multiplicative topological phases for an alternative to braiding-based topological quantum computation schemes, in which gate operations are performed through topological phase transitions. Published by the American Physical Society 2024
The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches to solving these problems. Various theoretical schemes for building topological quantum computation have been proposed. However, experimental implementation has always been a great challenge because it has proved to be extremely difficult to create and manipulate topological qubits in real systems. Therefore, topological quantum computation has not been realized in experiments yet. Here, we report the first experimental realization of topological quantum computation with electric circuits. Based on our proposed new scheme with circuits, Majorana-like edge states are not only observed experimentally, but also T junctions are constructed for the braiding process. Furthermore, we demonstrate the feasibility of topological quantum computing through a set of one- and two-qubit unitary operations. Finally, our implementation of Grover's search algorithm demonstrates that topological quantum computation is ideally suited for such tasks.
Abstract We propose the Hopf soliton vacuum --- the topological field-theoretic framework of Papers I--XV --- as a 3+1-dimensional platform for topological quantum computation (TQC). A qubit is encoded in the mutual linking number L∈{0,1}L \in \{0, 1\}L∈{0,1} of a Hopf soliton pair: ∣0⟩|0\rangle∣0⟩ corresponds to an unlinked pair, ∣1⟩|1\rangle∣1⟩ to a linked pair. Since linking number is an integer topological invariant, the qubit is passively protected against decoherence --- errors require reconnection events exponentially suppressed at energies below the soliton mass gap Δ\DeltaΔ. The SU(2)1_11​ Chern-Simons theory governing the Hopf vacuum (Paper V) provides the R-matrix R=eiπ/4R = e^{i\pi/4}R=eiπ/4 for soliton exchange, yielding Abelian (semionic) braiding. While SU(2)1_11​ alone is not universal, the 3+1D loop braid group provides additional operations (leapfrogging) beyond 2+1D braiding, and universality can be achieved via magic state distillation. We construct a gate set from soliton self-linking (single-qubit rotations) and inter-pair braiding (entangling gates), showing that topological protection yields error rates exponentially small in the ratio of system size to correlation length. Physical implementations include liquid crystal Hopfions, BEC vortex knots, and photonic topological states. This is a theoretical proposal: no experimental realization currently exists. > [!warning] Speculative Content > This paper is a theoretical proposal. The identification of Hopf soliton pairs as a TQC platform is new and untested. Standard TQC theory (Kitaev, Freedman et al., Nayak et al.) is well-established; the application to Hopf solitons is speculative. We clearly distinguish established results from proposals throughout. Keywords physics quantum computing topology anyons braiding TQC hopf solitons Type Preprint License CC BY 4.0 Date 2026-03-22 Subject Theoretical Physics DOI 10.5281/zenodo.19108219 © 2026 Alexander Novickis. Licensed under Creative Commons Attribution 4.0 International.
Qubits built out of Majorana zero modes constitute the primary path toward topologically protected quantum computing. Simulating the braiding process of multiple Majorana zero modes corresponds to the quantum dynamics of a superconducting many-body system. It is crucial to study the Majorana dynamics both in the presence of all other quasiparticles and for reasonably large system sizes. We present a method to calculate arbitrary many-body wave functions as well as their expectation values, correlators, and overlaps from time evolved single-particle states of a superconductor, allowing for significantly larger system sizes. We calculate the fidelity, transition probabilities, and joint parities of Majorana pairs to track the quality of the braiding process. We show how the braiding success depends on the speed of the braid. Moreover, we demonstrate the topological CNOT two-qubit gate as an example of two-qubit entanglement. Our Letter opens the path to test and analyze the many theoretical implementations of Majorana qubits. Moreover, this method can be used to study the dynamics of any noninteracting superconductor.
I point out that a possible minimal setting to realize Kitaev's proposal of a Topological Quantum Computation which offers topological protection from decoherence could in principle be realized by braided Majorana qubits. Majorana qubits and their braiding were introduced in Nucl. Phys. B 980, 115834 (2022) and further analyzed in J. Phys. A: Math. Theor. 57, 435203 (2024). Braided Majorana qubits implement a Gentile-type parastatistics with at most s-1 excited states accommodated in a multiparticle sector (the integer s=2,3,4,... labels quantum group reps at roots of unity). It is argued that braided Majorana qubits could play, for topological quantum computers, the same role as standard bits for ordinary computers and as qubits for "ordinary" quantum computers.