Abstract
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due to the technical limitations of current experimental platforms. Here, we take a state perpetration approach to mimic anyons in the toric code using a seven-qubit nuclear magnetic resonance quantum simulator. Anyons are created by dynamically preparing the ground and excited states of a seven-qubit planar version of the toric code, and are subsequently braided along two distinct, but topologically equivalent paths. We observe that the phase acquired by the anyons is independent of the path, and coincides with the ideal theoretical predictions when decoherence and implementation errors are taken into account. As the first demonstration of the topological path independence of anyons, our experiment helps to study and exploit the anyonic properties towards the goal of building a topological quantum computer.
Highlights
It is a fundamental question to investigate the physical properties of exchanging two identical particles
Through the quantum simulation approach [20,21,22,23,24,25,26,27,28,29,30], in which the experimental setup acts as a processor to mimic the dynamics of anyonic systems, several experiments have been implemented to demonstrate the exotic properties of anyons in small systems [16,17,18,19]
We study a seven-qubit system with three different paths to braid anyons: two non-trivial paths where the wave function picks up the π phase, and one trivial path where the wave function remains unchanged
Summary
It is a fundamental question to investigate the physical properties of exchanging two identical particles. Through the quantum simulation approach [20,21,22,23,24,25,26,27,28,29,30], in which the experimental setup acts as a processor to mimic the dynamics of anyonic systems, several experiments have been implemented to demonstrate the exotic properties of anyons in small systems [16,17,18,19] These experiments provide better understanding of braiding operations in realistic noise, opening up the possibility of fully utilizing the advantages of anyonic fractional statistics. We use a seven-qubit NMR quantum simlulator to realize the three braiding paths through the state preparation approach, and observe that the two phases acquired during the two non-trivial loops agree within experimental uncertainty, they are below the theoretical value of π. We account for experimental deviations from the theoretical predictions using numerical simulations that take realistic error sources into account
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