广义各向异性交换哈密顿量的编码普适性
Encoded Universality for Generalized Anisotropic Exchange Hamiltonians
摘要：
我们推导出一个编码的普遍性表示的广义各向异性交换哈密顿量，其中包含交叉产品的条款，除了通常的两粒子交换条款。利用最近发展起来的代数方法，证明了一个逻辑量子比特的最小普适性生成编码是基于三个物理量子比特的。我们展示了如何生成单量子比特和双量子比特操作的逻辑量子比特，使用适当的定时共轭运算来自分析的换向器代数。的操作的时间被认为是至关重要的，在允许简化的门序列的广义哈密顿量的形式类似于先前推导的对称（XY）各向异性交换哈密顿量。控制Z门到局部变换所需的操作总数为5。提出了一种可扩展的体系结构。
英文摘要：
We derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to show that the minimal universality-generating encodings of one logical qubit are based on three physical qubits. We show how to generate both single- and two-qubit operations on the logical qubits, using suitably timed conjugating operations derived from analysis of the commutator algebra. The timing of the operations is seen to be crucial in allowing simplification of the gate sequences for the generalized Hamiltonian to forms similar to that derived previously for the symmetric (XY) anisotropic exchange Hamiltonian. The total number of operations needed for a controlled-Z gate up to local transformations is five. A scalable architecture is proposed.
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