Related papers: Geometric representations of braid and Yang-Baxter…
Complete solution, more precisely, all invertible $4\times 4$ matrices $R,Q$ that solve Yang--Baxter system related to quantised braided groups, quantum doubles and other systems are given.
Many well-known and well-studied four by four universal quantum logic gates in the literature are of a specific form, the so called eight-vertex form \eqref{8vertexform} \cite{kaufman etal 05-1,kaufman etal 05-2}, or {\it similar} to it. We…
Given a rack Q and a ring A, one can construct a Yang-Baxter operator c_Q: V tensor V --> V tensor V on the free A-module V = AQ by setting c_Q(x tensor y) = y tensor x^y for all x,y in Q. In answer to a question initiated by D.N. Yetter…
A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer…
We study the Yang-Baxter equation for the $R$-matrices of the six-vertex model. We analyze the solutions and give new parametrizations of the Yang-Baxter equation. In particular, we find the maximal commutative families of parametrized…
The number of qubits in current quantum computers is a major restriction on their wider application. To address this issue, Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
In this work, we report on a novel quantum gate approximation algorithm based on the application of parametric two-qubit gates in the synthesis process. The utilization of these parametric two-qubit gates in the circuit design allows us to…
Integrable quantum computation is defined as quantum computing via the integrable condition, in which two-qubit gates are either nontrivial unitary solutions of the Yang--Baxter equation or the Swap gate (permutation). To make the…
We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of solutions to the Yang-Baxter equation and their associated…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…
We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a…
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
Motivated by recent findings on the derivation of parametric non-involutive solutions of the Yang-Baxter equation we reconstruct the underlying algebraic structures, called near braces. Using the notion of the near braces we produce new…
While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to…
The purpose of this paper is to present an interpretation for the decomposition of the tensor product of two or more irreducible representations of GL(N) in terms of a system of quantum particles. Our approach is based on a certain…
We establish a one-to-one correspondence between structure groups of non-degenerate, involutive and braided "set-theoretical" solutions of the quantum Yang-Baxter equation and Garside groups with a certain presentation. Moreover, we show…
We review the Yang-Baxterization process of braid group representations. We discuss the corresponding $n$-CB algebras in the Yang-Baxterization process. We present diagrams of the relations for the $4$-CB algebras. These relations are…