基态是量子计算通用资源的简单最近邻两体哈密顿系统
A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
摘要：
我们提出了一个简单的量子多体系统-一个二维量子位格，其哈密顿量由最近邻的两体相互作用组成-使得基态是使用单量子位测量的量子计算的通用资源。这种基态近似于被编码成更大数量的物理量子比特的簇状态。我们使用的哈密顿量是由投射的纠缠对态激发的，它提供了一种透明的机制来产生类似于基态的正方形或其他晶格结构上的编码簇态（以及各种其他量子态）。我们表明，在这种近似的错误采取的形式独立的错误债券发生固定的概率。这种系统的能隙，这在一定程度上决定了它的有用性的量子计算，被证明是独立的晶格的大小。此外，我们表明，这个能隙的缩放的耦合常数的哈密顿量是直接由晶格几何形状。因此，在六边形晶格（对于量子计算也是通用的资源）上获得的近似编码的簇状态可以被示出为具有比具有等效哈密顿量的正方形晶格上的一个更大的能隙。
英文摘要：
We present a simple quantum many-body system - a two-dimensional lattice of qubits with a Hamiltonian composed of nearest-neighbor two-body interactions - such that the ground state is a universal resource for quantum computation using single-qubit measurements. This ground state approximates a cluster state that is encoded into a larger number of physical qubits. The Hamiltonian we use is motivated by the projected entangled pair states, which provide a transparent mechanism to produce such approximate encoded cluster states on square or other lattice structures (as well as a variety of other quantum states) as the ground state. We show that the error in this approximation takes the form of independent errors on bonds occurring with a fixed probability. The energy gap of such a system, which in part determines its usefulness for quantum computation, is shown to be independent of the size of the lattice. In addition, we show that the scaling of this energy gap in terms of the coupling constants of the Hamiltonian is directly determined by the lattice geometry. As a result, the approximate encoded cluster state obtained on a hexagonal lattice (a resource that is also universal for quantum computation) can be shown to have a larger energy gap than one on a square lattice with an equivalent Hamiltonian.
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