New series of multi-parametric solutions to GYBE: quantum gates and integrability

Abstract

We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented for the inhomogeneous GYBEs. The first series of the solutions includes as particular cases the $X$-shaped trigonometric braiding matrices. For construction of the second series the colored and graded permutation operators are defined, and multi-spectral parameter Yang-Baxterization is performed. For some examples the corresponding integrable models are discussed. The unitary solutions existing in these two series can be considered as generalizations of the multipartite Bell matrices in the quantum information theory.

arXiv comment41 pages, 3 figures; edited

References in corpus (19)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Non-Abelian Anyons and Topological Quantum Computation
• Mixed State Entanglement and Quantum Error Correction
• Unpaired Majorana fermions in quantum wires
• Measurement-based quantum computation with cluster states
• Quantum Inverse Scattering Method and Correlation Functions
• Bosonic Quantum Codes for Amplitude Damping
• Braiding Operators are Universal Quantum Gates
• Comparing Quantum Entanglement and Topological Entanglement
• Berry phase and quantum criticality in Yang--Baxter systems
• Fermionic representations of integrable lattice systems
• On the solutions of the Yang-Baxter equations with general inhomogeneous eight-vertex $R$-matrix: Relations with Zamolodchikov's tetrahedral algebra
• On the solutions to the multi-parametric Yang-Baxter equations
• Braiding quantum gates from partition algebras
• Characteristics of 2D lattice models from fermionic realization: Ising and $XYZ$ models
• Solutions to the Yang-Baxter equations with $os{p}_q(1|2)$ symmetry: Lax operators
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
• ${\ell }_1$-norm and entanglement in screening out braiding from Yang-Baxter equation associated with ${\mathbb{Z}}_3$ parafermion
• Series of the solutions to Yang-Baxter equations: Hecke type matrices and descendant R-, L-operators

Cited by in corpus (1)

• Periodic Motzkin chain: Ground states and symmetries