论文标题
拓扑演变的图表上的量子概率空间
Quantum Probabilistic Spaces on Graphs for Topological Evolutions
论文作者
论文摘要
我们首先考虑在2D表面上演变的任何一个颗粒的融合规则，而A HyperGroup随附以构建纠缠的量子Markov链。 Fusion规则诱导了与基林参数及其双重相交数字的关联方案。将这些方案视为编码可能量子步行路径的常规图（自动形态）的一种有用方法。我们认为将Anyons的统一动力学描述为图形的统一动力学的编织B3。融合所引起的动力学（以及伴随分裂操作）可以看作是链在生长的图上演变而成的链，而编织为固定图上的自动形态。在我们的量子概率框架中，可以编码量子模拟算法含量的单位的无限迭代，如果允许粒子在更长的时间内相干地进化，则可以优雅地描述渐近造型。我们将在Bose-Mesner代数上定义量子状态，该代数也是Von Neumann代数以及Frobenius代数，以建立量子马尔可夫链，为拓扑计算提供了另一种观点。
We start with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains. The fusion rules induce an association scheme with Krein parameters and their duals the intersection numbers. One useful way to think of the schemes as regular graphs encoding the paths of possible quantum walks (automorphisms). We consider braid B3 that describes the unitary dynamics of the anyons as the automorphism subgroup of the graphs. The dynamics induced by the fusions (and the adjoint splitting operations) may be viewed as the chain evolving on a growing graph and the braiding as automorphisms on a fixed graph. In our quantum probability framework infinite iterations of the unitaries, which can encode algorithmic content for quantum simulations, can describe asymptotics elegantly if the particles are allowed to evolve coherently for a longer period. We will define quantum states on the Bose-Mesner algebra which is also a von Neumann algebra as well as a Frobenius algebra to build the quantum Markov chains providing another perspective to topological computation.
