论文标题
物质量子阶段中受对称保护的标志问题和魔术
Symmetry-protected sign problem and magic in quantum phases of matter
论文作者
论文摘要
我们介绍了对称性保护的符号问题和对称性保护的魔法的概念，以研究物质受对称保护拓扑（SPT）阶段的复杂性。特别是，我们说，如果由对称门组成的有限深度量子电路无法分别将状态转化为非负实际波函数或稳定状态，则具有对称性保护的符号问题或对称性保护的魔法。我们证明属于某些SPT阶段的状态具有这些特性，这是由于它们在边界上的异常对称作用。例如，我们发现一维的$ \ mathbb {z} _2 \ times \ times \ mathbb {z} _2 $ spt状态（例如群集状态）具有对称性保护的符号问题，并且二维$ \ \ \ mthbb {z} _2 $ spt States _2 $ spt States（E.G. Levin-levin-levin-leven-levin-gu state syms ocical sym sym sym sompted）此外，我们评论了对称性保护的符号问题与一维SPT状态的计算线特性之间的关系。在附录中，我们还引入了SPT阶段的显式装饰域墙模型，这可能引起独立感兴趣。
We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional $\mathbb{Z}_2 \times \mathbb{Z}_2$ SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional $\mathbb{Z}_2$ SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.
