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.

10 pages and 6 figures

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• Non-Abelian Anyons and Topological Quantum Computation
• Benchmarking quantum control methods on a 12-qubit system
• Liquid State NMR as a Test-bed for Developing Quantum Control Methods
• Dynamics and Control of a Quasi-1D Spin System
• Spin squeezing in an ensemble of quadrupolar nuclei NMR system
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• Compiling gate networks on an Ising quantum computer
• Preparing pseudo-pure states with controlled-transfer gates

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• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Optimal realization of Yang-Baxter gate on quantum computers
• QuYBE -- An Algebraic Compiler for Quantum Circuit Compression
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• Intrinsic bounds of a two-qudit random evolution
• Tails of Instability and Decay: a Hydrodynamic Perspective
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction