论文标题
超对称和量子计算
Supersymmetry and Quantum Computation
论文作者
论文摘要
讨论了超对称性与经典计算之间的相互作用。首先，结果表明，计算$ \ MATHCAL N \ LEQ 2 $量子机械系统的Witten索引的问题是$ \＃p $ - complete，因此很难解决。然后，引入了量子和超对称量子电路的超对称性概念，并讨论了它们的某些特性。特别是，结果表明，这些定义了具有稳定性特性的量子算法的非平凡子类。讨论了混凝土示例，包括超对称SYK模型和费米昂硬核模型。提出了一些应用和开放问题。
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore intractable. Then, the notions of supersymmetry in the space of qubits and supersymmetric quantum circuits are introduced and some of their properties discussed. In particular, it is shown that these define a nontrivial subclass of quantum algorithms with robustness properties typical of supersymmetric systems. Concrete examples, including the supersymmetric SYK model and fermion hard-core models are discussed. Some applications and open questions are suggested.
