自旋为1/2的粒子在具有最近邻相互作用的二维晶格上运动可以实现自主量子计算机
Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
摘要：
什么是最简单的哈密顿量，可以实现量子计算，而不需要任何控制操作在计算过程中？在以前的论文中，我们已经构建了一个10-本地有限程相互作用的量子比特之间的二维晶格具有这种性质。在这里，我们表明，在二维晶格上qutrits之间的配对相互作用是足够的，也可以实现一个遍历的计算机，其中的结果可以读出的时间平均状态后，一些后选择具有高的成功概率。其中两个量子态是由自旋为1/2的粒子的两个能级位于特定的晶格位置给出的，第三个量子态是它的不存在。相邻粒子间的相互吸引力和跳跃项共同作用引起耦合量子行走，其中粒子自旋受到空间非均匀相互作用，实现完整量子计算。完整方法确保所实现的电路不依赖于行走所需的时间。尽管所需类型的自旋-自旋相互作用的实现目前还不清楚，但该模型表明，相当简单的哈密顿量足够强大，可以在封闭的物理系统中进行通用的量子计算。
英文摘要：
What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a 10-local finite-range interaction among qubits on a 2D lattice having this property. Here we show that pair-interactions among qutrits on a 2D lattice are sufficient, too, and can also implement an ergodic computer where the result can be read out from the time average state after some post-selection with high success probability. Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle located at a specific lattice site, the third state is its absence. Usual hopping terms together with an attractive force among adjacent particles induce a coupled quantum walk where the particle spins are subjected to spatially inhomogeneous interactions implementing holonomic quantum computing. The holonomic method ensures that the implemented circuit does not depend on the time needed for the walk. Even though the implementation of the required type of spin-spin interactions is currently unclear, the model shows that quite simple Hamiltonians are powerful enough to allow for universal quantum computing in a closed physical system.
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