A probabilistic evolutionary optimization approach to compute quasiparticle braids
This work addresses the challenge of efficient gate implementation in topological quantum computing, offering incremental improvements in braid optimization.
The paper tackles the problem of finding optimal braids for topological quantum gates by proposing estimation of distribution algorithms, achieving solutions with accuracy around 10^-6 and lengths up to 9 times shorter than existing methods.
Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because these are not Abelian, the problem can be reduced to finding an optimal product of braid generators where the optimality is defined in terms of the gate approximation and the braid's length. In this paper we propose the use of different variants of estimation of distribution algorithms to deal with the problem. Furthermore, we investigate how the regularities of the braid optimization problem can be translated into statistical regularities by means of the Boltzmann distribution. We show that our best algorithm is able to produce many solutions that approximates the target gate with an accuracy in the order of $10^{-6}$, and have lengths up to 9 times shorter than those expected from braids of the same accuracy obtained with other methods.