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:2405.20950 · Physical Review Research

Quantum computation with hybrid parafermion-spin qubits

Denis V. Kurlov, Melina Luethi, Anatoliy I. Lotkov, Katharina Laubscher, Jelena Klinovaja, Daniel Loss

Published Jul 8, 2025• 1 citation
arXivHTMLPDF

Abstract

We propose a universal set of single- and two-qubit quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit to a Z 2 m parafermion qubit with arbitrary integer m . The special case m = 1 reproduces the results previously derived for Majorana qubits. Our formalism utilizes Fock parafermions, facilitating a transparent treatment of hybrid parafermion-spin systems. Furthermore, we highlight the previously overlooked importance of particle-hole symmetry in these systems. We give concrete examples how the hybrid qubit system could be realized experimentally for Z 4 and Z 6 parafermions. In addition, we discuss a simple readout scheme for the fractional parafermion charge via the measurement of the spin-qubit resonant frequency.

DOI
10.1103/7cd9-c7yc

Related papers

Universal quantum computation with hybrid spin-Majorana qubits

Silas Hoffman, Constantin Schrade, Jelena Klinovaja +1 more

We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum-dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot that is tunnel coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid cnot gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a cnot gate is implemented that acts on neighboring Majorana qubits and eliminates the necessity of interqubit braiding. In both setups, the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a swap or hybrid swap gate which is sufficient for universal quantum computation without projective measurements.

arXiv:1602.06923•Physical review. B./Physical review. B•Jul 25, 2016•106 citations

Quantum computing with parafermions

Adrian Hutter, Daniel Loss

${\mathbb{Z}}_{d}$ parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case $d=2$. In contrast to Majorana fermions, braiding of parafermions with $d>2$ allows one to perform an entangling gate. This has spurred interest in parafermions, and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a family of $2d$ representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a $d$-level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows one to generate the entire single-qudit Clifford group (up to phases), for any $d$. If $d$ is odd, then we show that in fact the entire many-qudit Clifford group can be generated.

arXiv:1511.02704•Physical review. B./Physical review. B•Mar 2, 2016•70 citations

Qubits as parafermions

Lian-Ao Wu, Daniel A. Lidar

Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a classification of the algebras of operators acting on qubits. These algebras in turn classify the universality of different classes of physically relevant qubit-qubit interaction Hamiltonians. The mapping is further used to elucidate the connections between qubits, bosons, and fermions. These connections allow us to share universality results between the different particle types. Finally, we use the mapping to study the quantum computational power of certain anisotropic exchange Hamiltonians. In particular, we prove that the XY model with nearest-neighbor interactions only is not computationally universal. We also generalize previous results about universal quantum computation with encoded qubits to codes with higher rates.

arXiv:quant-ph/0109078•Journal of Mathematical Physics•Sep 1, 2002•63 citations

Quantum Gates Built on a Spin Qubit and a Kitaev Parity Qubit

Zhi-Hai Liu, Jiang Zhang, Guilu Long +1 more

Spin is typically traced out in the description of quantum-dot-based Kitaev chains to simplify the construction of Majorana fermions. Yet the intrinsic spin structure of poor-man's Majorana modes in minimal Kitaev chains under finite Zeeman fields offers a natural interface for the Kitaev parity qubit to interact with other spinful systems. Here, we establish such a platform to bridge the parity qubit and a quantum-dot spin qubit, with the effective coupling governed by the spin-dependent delocalization of the Majorana modes. Depending on whether the spin qubit is coupled to one or two chains constituting the parity qubit, the parity-spin coupling exhibits distinct forms: an anisotropic parity-conserving exchange interaction or a nontrivial exchange tensor tunable via the interchain superconducting-phase bias. Leveraging fast spin-qubit manipulation, we further demonstrate universal parity-qubit control, high-fidelity qubit-state readout, and entangling operations between the parity and spin qubits. These results turn the spinful structure of poor-man's Majoranas from a finite-field imperfection into a resource for hybrid quantum control.

arXiv:2609.28924•Sep 24, 2026•0 citations

Universal quantum computing with correlated spin-charge states

Jordan Kyriakidis, Guido Burkard

We propose a universal quantum computing scheme in which the orthogonal qubit states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot, and gate operations are induced all electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge properties of the \ensuremath{\mid}0⟩, \ensuremath{\mid}1⟩ states, the lowest-order relaxation and decoherence rates $1∕{T}_{1}$ and $1∕{T}_{2}$, within the Born-Markov approximation, both vanish for a large class of environmental couplings. We give explicit pulse sequences for a universal set of gates (phase, $\ensuremath{\pi}∕8$, Hadamard, and CNOT) and discuss state preparation, manipulation, and detection.

arXiv:cond-mat/0606627•Physical Review B•Mar 26, 2007•21 citations

A fast quantum interface between spin qubits of different codes

Akito Noiri, Takashi Nakajima, Jun Yoneda +11 more

Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.

•Apr 13, 2018•0 citations
We propose a universal set of single- and two-qubit quantum gates acting on a hybrid qubit formed by coupling a quantum dot spin qubit to a Z 2 m parafermion qubit with arbitrary integer m . The special case m = 1 reproduces the results previously derived for Majorana qubits. Our formalism utilizes Fock parafermions, facilitating a transparent treatment of hybrid parafermion-spin systems. Furthermore, we highlight the previously overlooked importance of particle-hole symmetry in these systems. We give concrete examples how the hybrid qubit system could be realized experimentally for Z 4 and Z 6 parafermions. In addition, we discuss a simple readout scheme for the fractional parafermion charge via the measurement of the spin-qubit resonant frequency.
We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum-dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot that is tunnel coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid cnot gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a cnot gate is implemented that acts on neighboring Majorana qubits and eliminates the necessity of interqubit braiding. In both setups, the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a swap or hybrid swap gate which is sufficient for universal quantum computation without projective measurements.
Zd{\mathbb{Z}}_{d}Zd​ parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case d=2d=2d=2. In contrast to Majorana fermions, braiding of parafermions with d>2d>2d>2 allows one to perform an entangling gate. This has spurred interest in parafermions, and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a family of 2d2d2d representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a ddd-level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows one to generate the entire single-qudit Clifford group (up to phases), for any ddd. If ddd is odd, then we show that in fact the entire many-qudit Clifford group can be generated.
Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a classification of the algebras of operators acting on qubits. These algebras in turn classify the universality of different classes of physically relevant qubit-qubit interaction Hamiltonians. The mapping is further used to elucidate the connections between qubits, bosons, and fermions. These connections allow us to share universality results between the different particle types. Finally, we use the mapping to study the quantum computational power of certain anisotropic exchange Hamiltonians. In particular, we prove that the XY model with nearest-neighbor interactions only is not computationally universal. We also generalize previous results about universal quantum computation with encoded qubits to codes with higher rates.
Spin is typically traced out in the description of quantum-dot-based Kitaev chains to simplify the construction of Majorana fermions. Yet the intrinsic spin structure of poor-man's Majorana modes in minimal Kitaev chains under finite Zeeman fields offers a natural interface for the Kitaev parity qubit to interact with other spinful systems. Here, we establish such a platform to bridge the parity qubit and a quantum-dot spin qubit, with the effective coupling governed by the spin-dependent delocalization of the Majorana modes. Depending on whether the spin qubit is coupled to one or two chains constituting the parity qubit, the parity-spin coupling exhibits distinct forms: an anisotropic parity-conserving exchange interaction or a nontrivial exchange tensor tunable via the interchain superconducting-phase bias. Leveraging fast spin-qubit manipulation, we further demonstrate universal parity-qubit control, high-fidelity qubit-state readout, and entangling operations between the parity and spin qubits. These results turn the spinful structure of poor-man's Majoranas from a finite-field imperfection into a resource for hybrid quantum control.
We propose a universal quantum computing scheme in which the orthogonal qubit states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩ are identical in their single-particle spin and charge properties. Each qubit is contained in a single quantum dot, and gate operations are induced all electrically by changes in the confinement potential. Within the computational space, these qubits are robust against environmental influences that couple to the system through single-particle channels. Due to the identical spin and charge properties of the \ensuremath{\mid}0⟩, \ensuremath{\mid}1⟩ states, the lowest-order relaxation and decoherence rates 1∕T11∕{T}_{1}1∕T1​ and 1∕T21∕{T}_{2}1∕T2​, within the Born-Markov approximation, both vanish for a large class of environmental couplings. We give explicit pulse sequences for a universal set of gates (phase, $\ensuremath{\pi}∕8$, Hadamard, and CNOT) and discuss state preparation, manipulation, and detection.
Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.