twists are defects in the lattice which can be utilized to perform computations on encoded data. twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. they are known to exhibit projective non-abelian statistics which is exploited to perform encoded gates. in this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. to the best of our knowledge, this is the first study of twists in qudit color codes. specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. we also present a mapping between generalized pauli operators and strings in the lattice. making use of the construction, we give protocols to implement generalized clifford gates using charge-color permuting twists.twists are defects in the lattice which can be utilized to perform computations on encoded data. twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. they are known to exhibit projective non-abelian statistics which is exploited to perform encoded gates. in this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. to the best of our knowledge, this is the first study of twists in qudit color codes. specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. we also present a mapping between generalized pauli operators and strings in the lattice. making use of the construction, we give protocols to implement generalized clifford gates using charge-color permuting twists.

Oct 16, 20210 citations

Quantum computation with charge-and-color-permuting twists in qudit color codes

Manoj G. Gowda, Pradeep Kiran Sarvepalli

Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes, and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics, which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over the odd prime alphabet. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes, and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics, which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over the odd prime alphabet. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.

arXiv:2110.08680Physical Review AFeb 24, 20222 citations

Qudit Twisted-Torus Codes in the Bivariate Bicycle Framework

Mourad Halla

We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that, within the bivariate-bicycle viewpoint, twisting generalized toric patterns can significantly improve the finite-size distance of qubit codes. Building on this insight, we extend the construction and the search to qudit codes over finite fields. Using algebraic methods based on Laurent-polynomial ideals and Gröbner-basis computations over $\mathbb{F}_q$ , we compute the number of logical qudits on any twisted torus and identify compact codes with favorable rate--distance tradeoffs. Overall, for the finite sizes explored, twisted-torus qudit constructions typically achieve larger estimated distances than their untwisted counterparts and, at the same number of physical and logical qudits, larger estimated distances than previously reported twisted qubit instances. The best new codes are tabulated.We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that, within the bivariate-bicycle viewpoint, twisting generalized toric patterns can significantly improve the finite-size distance of qubit codes. Building on this insight, we extend the construction and the search to qudit codes over finite fields. Using algebraic methods based on Laurent-polynomial ideals and Gröbner-basis computations over $\mathbb{F}_q$, we compute the number of logical qudits on any twisted torus and identify compact codes with favorable rate--distance tradeoffs. Overall, for the finite sizes explored, twisted-torus qudit constructions typically achieve larger estimated distances than their untwisted counterparts and, at the same number of physical and logical qudits, larger estimated distances than previously reported twisted qubit instances. The best new codes are tabulated.

quant-pharXiv:2602.04443Feb 5, 20260 citations

Qubit Chip

Graham P. Collins

Scientific AmericanAug 1, 19990 citations

The qubit duet

G. Blatter

NatureFeb 1, 20035 citations

\mathbb{F}_q

, we compute the number of logical qudits on any twisted torus and identify compact codes with favorable rate--distance tradeoffs. Overall, for the finite sizes explored, twisted-torus qudit constructions typically achieve larger estimated distances than their untwisted counterparts and, at the same number of physical and logical qudits, larger estimated distances than previously reported twisted qubit instances. The best new codes are tabulated.