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.
Highlights
In recent years, the Yang-Baxter equation (YBE)[1,2,3,4], an important tool in theoretical physics, has attracted much attention in the context of quantum information science
Nuclear Magnetic Resonance (NMR) implementations of quantum information processors are usually executed in an ensemble of identical and non-interacting molecules at room temperature, where nuclear spins are employed as qubits
The observed signal from a NMR system in the above state (2), called a pseudo-pure state (PPS), is equivalent to that from a system in a pure state, except that the PPS signal strength is reduced by a factor ε
Summary
The Yang-Baxter equation (YBE)[1,2,3,4], an important tool in theoretical physics, has attracted much attention in the context of quantum information science. In (1 + 1)-dimensional quantum field theory/scattering theory the YBE means that the process of 3-particle scattering is reduced to a sequence of pairwise collisions which do not depend on the time ordering of the 2-body collisions[10] In this case R is interpreted as the two-body scattering matrix (usually denoted S-matrix) and the Yang-Baxter Equation has the name of “factorization equation”. On a more recent note, there has been a considerable increase of investigation of these structures related to quantum integrability due to several new exact results that are playing an important role in the progress of our understanding of the AdS/CFT correspondence[11] It is worth mentioning, in addition, the interest raised by the realization of integrable systems, in ultracold physics[12,13]. The interest in this form comes from its relation to the braid group which has been recently linked to topological quantum computation[6,7,8] and a scheme for its verification through an optical setup has been proposed[17] and achieved[18]
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