Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
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Padmanabhan, Pramod (ORCID:0000000285776312)↗
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Solutions of the Quantum Yang-Baxter Equations Associated with (1-3/2)-D Representations of SU(sub q) (2)
The solutions of the spectral independent QYBE associated with (1-3/2)-D representations of SU(sub q) (2) are derived, based on the weight conservation and extended Kauffman diagrammatic technique. It is found that there are nonstandard solutions.
Yijun, Huang↗
Covariant deformed oscillator algebras
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Quesne, Christiane↗
There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)
It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.
Yijun, Huang↗
Hybrid algorithm for the time-dependent Hartree–Fock method using the Yang–Baxter equation on quantum computers *
Abstract The time-dependent Hartree–Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single Slater determinants. One of the major advantages of performing time dynamics within Hartree–Fock theory is the free fermionic nature of the problem, which makes TDHF classically simulatable in polynomial time. Here, we present a hybrid TDHF implementation for quantum computers. This quantum circuit grows with time; but with our recent work on circuit compression via the Yang–Baxter equation (YBE), the resulting circuit is constant depth. This study provides a new way to simulate TDHF with the aid of a quantum device as well as provides a new direction for the application of YBE symmetry in quantum chemistry simulations.
97 MATHEMATICS AND COMPUTING↗