Experimental realization of the Yang-Baxter Equation via NMR interferometry

Abstract

The Yang-Baxter equation is an important tool in theoretical physics, with many applications in different domains that span from condensed matter to string theory. Recently, the interest on the equation has increased due to its connection to quantum information processing. It has been shown that the Yang-Baxter equation is closely related to quantum entanglement and quantum computation. Therefore, owing to the broad relevance of this equation, besides theoretical studies, it also became significant to pursue its experimental implementation. Here, we show an experimental realization of the Yang-Baxter equation and verify its validity through a Nuclear Magnetic Resonance (NMR) interferometric setup. Our experiment was performed on a liquid state Iodotrifluoroethylene sample which contains molecules with three qubits. We use Controlled-transfer gates that allow us to build a pseudo-pure state from which we are able to apply a quantum information protocol that implements the Yang-Baxter equation.

Tails of Instability and Decay: a Hydrodynamic Perspective

“…Model and Hydrodynamic Equations.-Many new applications of 1+1D quantum integrable models has emerged over the past two decades. Originally regarded as toy models with rich underlying mathematical structures, they now play a role in many areas of modern theoretical physics: from the emergence of integrability in the context of string/gauge theories [19], to the experimental realisation of quantum integrable structures [20,21], to the resulting measurement of quantities that can be directly compared to analytic formulae [22,23]. The investigation of the out-of-equilibrium dynamical features of quantum integrable models, largely spurred by the Quantum Newton's Cradle experiment [24], has become an active area of research [25].…”

Yang–Baxter integrable models in experiments: from condensed matter to ultracold atoms

“…In the optics framework several proposals for simulating the Yang-Baxter equation have been discussed [106] and a first attempt to verify it has been conducted in [107] using linear quantum optical components such as beamsplitters, half-wave plates, quarterwave plates, etc. An experimental realisation of the Yang-Baxter equation through a Nuclear Magnetic Resonance interferometric setup has been performed on a liquid state Iodotrifluoroethylene sample of molecules containing three qubits [108], establishing an additional striking connection between integrability on the one hand and quantum information processing on the other. This opens up a way to implement quantum entanglement with integrability and certainly deserves to be further investigated.…”

The exact solution of a generalized two-spins model

“…More recently solvable models have also shown up in relation to string theories [22][23][24]. Remarkably it is important to mention that exactly solvable models are recently finding their way into the lab, mainly in the context of ultracold atoms [25][26][27][28][29][30][31] but also in nuclear magnetic resonance (NMR) experiments [32,33] becoming its study as well as the derivation of new models an even more fascinating field. We are considering in this work a multi-spins Lax operator that like the multi-bosons Lax operator in [34] permits to solve a family of models, helping to increase the number of integrable models solved by the algebraic Bethe ansatz method.…”

“…These spins cluster integrable models are important as for example in quantum computation and quantum information, quantum simulation using nuclear magnetic resonance (NMR) [35][36][37] or trapped ions [38] as well as in molecular magnetism [39]. Recently, spins configurations like these were proposed in [38] to a universal digital quantum simulation with trapped ions and an experimental realization of the Yang-Baxter equation was realized via NMR interferometry [32] using Iodotrifluoroethylene (C 2 F 3 I) molecules. Another important application of this spins configurations is as a spin network that appears in quantum gravity [40,41].…”