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

Journal of Experimental and Theoretical Physics Letters

Two-Qubit Operation on Majorana Qubits in Ordinary-Qubit Chains

Yu. Makhlin, Stefan Backens, Alexander Shnirman

Published Nov 28, 2018• 2 citations
Publisher

Abstract

Majorana zero modes can be simulated in structures based on spin or quasi-spin degrees of freedom, e.g., Josephson-qubit chains. Braiding of Majorana degrees of freedom is realized using T-junctions supplied with an auxiliary spin (ancilla). Motivated by prospective experiments, we analyze the braiding in the spin representation, which provides the basis for the analysis of imperfections characteristic to the spin and qubit designs. The result of the braiding operation is straightforwardly found for the initial basis states of the two qubits and the ancilla, up to phase factors. Here, we fix these phase factors and thus describe the complete two-qubit operation. This result is relevant for physical simulation of the Majorana qubits in Josephson-qubit chains and other spin or qubit structures.

DOI
10.1134/s0021364018230029

Related papers

Decoherence dynamics of Majorana qubits under braiding operations

Hon-Lam Lai, Wei-Min Zhang

We study the decoherence dynamics of Majorana qubit braiding operations in a T-junction topological superconducting chain (TSC) system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through Bogoliubon correlations formed by exchanging Majorana zero modes (MZMs) between two TSCs in braiding operations. We also demonstrate with the exact master equation how MZMs and also the Bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures. As a result, Majorana qubit coherence and also the fermion parity conservation cannot be immune from local perturbations during braiding operations.

arXiv:1909.13056•Physical review. B./Physical review. B•May 18, 2020•12 citations

Nonadiabatic braiding of Majorana modes

Fei Yu, P. Z. Zhao, Jiangbin Gong

The realization and manipulation of Majorana zero modes have drawn significant attention for their crucial role in enabling topological quantum computation. Conventional approaches to the braiding of Majorana zero modes rely on adiabatic processes. In this work, using a composite 2-Kitaev-chain system accommodating Majorana zero modes as a working example, we propose a nonadiabatic and non-Abelian geometry phase-based protocol to execute operations on these Majorana zero modes. This is possible by locally coupling the edge sites of both quantum chains with an embedded lattice defect, successfully simulating the braiding operation of two Majorana modes in a highly nonadiabatic fashion. To further enhance the robustness against control imperfections, we apply a multiple-pulse composite strategy to our quantum chain setting for second-order protection of the braiding operations. Our proposal can also support the fast and robust realization of the $\ensuremath{\pi}/8$ gate, an essential ingredient for universal quantum computation. This work hence offers a potential pathway toward the nonadiabatic and fault-tolerant control of Majorana zero modes.

arXiv:2503.00953•Physical review. B./Physical review. B•Aug 22, 2025•2 citations

Encoding a qubit with Majorana modes in superconducting circuits

J. Q. You, Z. D. Wang, Wenxian Zhang +1 more

Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.

arXiv:1108.3712•Scientific Reports•Jul 2, 2014•51 citations

Simulated non-Abelian statistics of Majorana zero modes from a Kitaev lattice

Foster Sabatino, Matthew Brooks, Charles Tahan +1 more

We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer. Rather than utilizing MZMs at the boundaries of quantum Ising chains, which are typically represented as nonlocal operators on a quantum computer, using a Kitaev lattice allows us to exploit a local representation of MZMs. We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian, i.e. physical qubit Hamiltonian. Projecting this onto a subspace of states, we extract an effective Hamiltonian which drives a non-Abelian Berry phase. Using several approximations, we construct a set of gates which mimics this accumulation of non-Abelian phase and process this construction on a quantum computer. For two and four MZMs, we realize braiding fidelities of approximately 85 and 47%, respectively.

arXiv:2503.15405•Physical review. B./Physical review. B•Jul 28, 2025•1 citation

Disentangled Quantum Operation on Majorana Qubits in Qubit Chains

Yu. Makhlin, Stefan Backens, Alexander Shnirman

Abstract We consider quantum logical gates on Majorana qubits implemented in chain structures of ordinary qubits, spins, or pseudospins. We demonstrate that one can implement a two-qubit operation via local manipulations, using an extra coupler spin in a T-junction geometry, so that this coupler spin remains disentangled from the qubit. Furthermore, we identify a set of symmetry operations, which not only allow us to determine the resulting two-qubit gate, but also to demonstrate robustness of the resulting gate to inaccuracies in the manipulations, known for topological quantum computation.

Journal of Experimental and Theoretical Physics•Oct 1, 2019•1 citation

Manipulating and probing Majorana fermions using superconducting circuits

J. Q. You, Z. D. Wang, Wenxian Zhang +1 more

Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.

•Aug 18, 2011•2 citations
Majorana zero modes can be simulated in structures based on spin or quasi-spin degrees of freedom, e.g., Josephson-qubit chains. Braiding of Majorana degrees of freedom is realized using T-junctions supplied with an auxiliary spin (ancilla). Motivated by prospective experiments, we analyze the braiding in the spin representation, which provides the basis for the analysis of imperfections characteristic to the spin and qubit designs. The result of the braiding operation is straightforwardly found for the initial basis states of the two qubits and the ancilla, up to phase factors. Here, we fix these phase factors and thus describe the complete two-qubit operation. This result is relevant for physical simulation of the Majorana qubits in Josephson-qubit chains and other spin or qubit structures.
We study the decoherence dynamics of Majorana qubit braiding operations in a T-junction topological superconducting chain (TSC) system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through Bogoliubon correlations formed by exchanging Majorana zero modes (MZMs) between two TSCs in braiding operations. We also demonstrate with the exact master equation how MZMs and also the Bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures. As a result, Majorana qubit coherence and also the fermion parity conservation cannot be immune from local perturbations during braiding operations.
The realization and manipulation of Majorana zero modes have drawn significant attention for their crucial role in enabling topological quantum computation. Conventional approaches to the braiding of Majorana zero modes rely on adiabatic processes. In this work, using a composite 2-Kitaev-chain system accommodating Majorana zero modes as a working example, we propose a nonadiabatic and non-Abelian geometry phase-based protocol to execute operations on these Majorana zero modes. This is possible by locally coupling the edge sites of both quantum chains with an embedded lattice defect, successfully simulating the braiding operation of two Majorana modes in a highly nonadiabatic fashion. To further enhance the robustness against control imperfections, we apply a multiple-pulse composite strategy to our quantum chain setting for second-order protection of the braiding operations. Our proposal can also support the fast and robust realization of the $\ensuremath{\pi}/8$ gate, an essential ingredient for universal quantum computation. This work hence offers a potential pathway toward the nonadiabatic and fault-tolerant control of Majorana zero modes.
Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.
We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer. Rather than utilizing MZMs at the boundaries of quantum Ising chains, which are typically represented as nonlocal operators on a quantum computer, using a Kitaev lattice allows us to exploit a local representation of MZMs. We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian, i.e. physical qubit Hamiltonian. Projecting this onto a subspace of states, we extract an effective Hamiltonian which drives a non-Abelian Berry phase. Using several approximations, we construct a set of gates which mimics this accumulation of non-Abelian phase and process this construction on a quantum computer. For two and four MZMs, we realize braiding fidelities of approximately 85 and 47%, respectively.
Abstract We consider quantum logical gates on Majorana qubits implemented in chain structures of ordinary qubits, spins, or pseudospins. We demonstrate that one can implement a two-qubit operation via local manipulations, using an extra coupler spin in a T-junction geometry, so that this coupler spin remains disentangled from the qubit. Furthermore, we identify a set of symmetry operations, which not only allow us to determine the resulting two-qubit gate, but also to demonstrate robustness of the resulting gate to inaccuracies in the manipulations, known for topological quantum computation.
Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.