论文标题
通用拓扑量子计算与Majorana Edge Modes紧密相关
Universal topological quantum computation with strongly correlated Majorana edge modes
论文作者
论文摘要
基于主要的量子门尚不完整用于执行通用拓扑量子计算，而基于斐波那契的大门很难以电子方式和几乎与常规量子电路模型相吻合。在参考\ cite {hukane}，已经表明，在手性拓扑超导体中，在fibobacci anyon $τ$中，在手性拓扑超导体中具有强度相关的Majorana边缘模式，而在Tricritical Ising模型中，均可分解为fibobacci $ \ varepsilon $。 $τ$和$ \ varepsilon $通过费米亚模式之间的反元素产生了Anyon {collisions}，并给出了$τ$或$ \ varepsilon $的编织。有了这些编织，完整的成员{}一组通用门，保利大门，哈达姆门和额外的相位门，用于1 Quition，以及2 Quibits的受控门，是拓扑的。编码量子信息并读取计算结果可以通过电信号执行。使用稀疏密度的混合编码，我们设置了量子电路{受控门发现{是}概率栅极}，并设计了用手性拓扑超导体的薄膜设计相应的设备。作为通用拓扑量子计算的一个示例，我们显示了Shor整数分解算法的应用。
Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In Ref. \cite{hukane}, it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibobacci anyon $τ$ and a thermal operator anyon $\varepsilon$ in the tricritical Ising model. The deconfinement of $τ$ and $\varepsilon$ via the interaction between the fermion modes yields the anyon {collisions} and gives the braiding of either $τ$ or $\varepsilon$. With these braidings, the complete members {of} a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for 1-qubit as well as controlled-not gate for 2-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit {where the controlled-not gate turns out { to be} a probabilistic gate} and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor's integer factorization algorithm.
