一种谢尔宾斯基三角形费米子到量子比特变换
A Sierpinski Triangle Fermion-to-Qubit Transform
AI总结：
本文基于新发现的 Sierpinski tree 数据结构提出一种费米子到量子比特编码，兼具 ternary tree 的算符局域性与计算基态表示优势。
摘要：
为了在量子计算机上模拟费米子系统，必须在量子比特上表示费米子态和算符。这可以通过多种方式实现，包括著名的 Jordan-Wigner 变换，以及 parity、Bravyi-Kitaev 和 ternary tree 编码。值得注意的是，Bravyi-Kitaev 编码可以用一种经典数据结构 Fenwick tree 来描述。在这里，我们建立了一类类似于 Fenwick tree 的经典数据结构与一类一一对应的费米子到量子比特变换之间的联系。我们提出了一种新颖的费米子到量子比特编码，该编码基于最近发现的“Sierpinski tree”数据结构，其算符局域性与 ternary tree 编码相匹配，并且还具有将费米子态编码为计算基态的额外优势。这类似于用 Fenwick tree 来表述 Bravyi-Kitaev 编码。
英文摘要：
In order to simulate a system of fermions on a quantum computer, it is necessary to represent the fermionic states and operators on qubits. This can be accomplished in multiple ways, including the well-known Jordan-Wigner transform, as well as the parity, Bravyi-Kitaev, and ternary tree encodings. Notably, the Bravyi-Kitaev encoding can be described in terms of a classical data structure, the Fenwick tree. Here we establish a correspondence between a class of classical data structures similar to the Fenwick tree, and a class of one-to-one fermion-to-qubit transforms. We present a novel fermion-to-qubit encoding based on the recently discovered "Sierpinski tree" data structure, which matches the operator locality of the ternary tree encoding, and has the additional benefit of encoding the fermionic states as computational basis states. This is analogous to the formulation of the Bravyi-Kitaev encoding in terms of the Fenwick tree.
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