论文标题
斐波那契anyons vs majora fermions
Fibonacci anyons versus Majorana fermions
论文作者
论文摘要
我们已经研究了$ {\ rm su}（2）_k $ Anyon型号，评估了他们的拓扑量子计算的前景。特别是，我们比较了Ising（$ k = 2 $）Anyon和fibonacci（$ k = 3 $）Anyon模型，这是由于它们基于Majoraana Fermion Quasiparticles或异国情调的分数量子座状状态的潜在实现的可能性。不同的Anyon模型的量子计算性能是通过目标单一操作员与Anyon Braiding实现的近似值之间的差异来量化的。为了促进有效的比较，我们开发了一种蒙特卡洛增强的Solovay-Kitaev量子编译器算法，该算法从指数较大的大型搜索树中找到了多项式时间中最佳的编织单词。由于单独编织在Ising Anyon模型中无法实现通用量子计算，因此我们引入了一个额外的基本相位门来对非本质的测量过程进行建模，该过程以破坏完整的拓扑保护的成本来恢复Anyon模型的通用性。我们通过将可控的噪声项引入所有非主观门操作来对传统的变质过程进行算法对算法进行建模。我们发现，对于合理水平的破坏水平，即使是混合动力模型也保留了比常规，非本质，量子计算机的重要拓扑优势。此外，我们发现，由于门噪声超出了$ 100 $基本编织订单的单词长度的固有误差，因此只有出人意料的简短编织的短短辫子才能进行编译。我们得出的结论是，混合拓扑量子计算的未来仍然很有希望。
We have studied ${\rm SU}(2)_k$ anyon models, assessing their prospects for topological quantum computation. In particular, we have compared the Ising ($k=2$) anyon and Fibonacci ($k=3$) anyon models, motivated by their potential for future realizations based on Majorana fermion quasiparticles or exotic fractional quantum-Hall states, respectively. The quantum computational performance of the different anyon models is quantified at single qubit level by the difference between a target unitary operator and its approximation realised by anyon braiding. To facilitate efficient comparisons, we have developed a Monte Carlo enhanced Solovay-Kitaev quantum compiler algorithm that finds optimal braid words in polynomial time from the exponentially large search tree. Since universal quantum computation cannot be achieved within the Ising anyon model by braiding alone, we have introduced an additional elementary phase gate to model a non-topological measurement process, which restores universality of the anyon model at the cost of breaking the full topological protection. We model conventional kinds of decoherence processes algorithmically by introducing a controllable noise term to all non-topological gate operations. We find that for reasonable levels of decoherence, even the hybrid Ising anyon model retains a significant topological advantage over a conventional, non-topological, quantum computer. Furthermore, we find that only surprisingly short anyon braids are ever required to be compiled due to the gate noise exceeding the intrinsic error of the braid words already for word lengths of the order of $100$ elementary braids. We conclude that the future for hybrid topological quantum computation remains promising.
