论文标题
用小光锥的量子电路的非本地计算
Non-local computation of quantum circuits with small light cones
论文作者
论文摘要
非本地量子计算的任务需要在两方之间仅具有一轮通信的两党之间的$ n $ Qubits实施统一，理想情况下，预先共享的纠缠最少。我们介绍了一种新协议，该协议利用了一个事实，即仅在少量量子位上完成时，基于端口的传送的成本要少得多。尽管以前的协议的纠缠成本与单一或缩放的复杂性无关，但新协议尺度的成本与单一的非本地性。具体而言，它采用$ \ sim n^{4v} $的表格，并带有$ v $，是实现单位的电路中过去光锥的最大体积。因此，我们可以使用多项式纠缠使用$ v \ sim o（1）$以及具有$ v \ sim \ sim \ mathrm {polylog}（n）$使用quasi polynomial纠缠的统一电路。对于一般的统一电路，$ d $层的$ k $ qubit门$ v $最多是$ k^d $，但是如果强加了几何区域，则最多是$ d $的多项式。我们给出了一类明确的单位，我们的协议的纠缠成本量表比任何已知的协议都要好。我们还表明，可以进行几个扩展，而不会显着影响纠缠成本 - 任意的本地预处理和后处理；全球克利福德预处理和后处理；以及添加多项式辅助系统的数量。
The task of non-local quantum computation requires implementation of a unitary on $n$ qubits between two parties with only one round of communication, ideally with minimal pre-shared entanglement. We introduce a new protocol that makes use of the fact that port-based teleportation costs much less entanglement when done only on a small number of qubits at a time. Whereas previous protocols have entanglement cost independent of the unitary or scaling with its complexity, the cost of the new protocol scales with the non-locality of the unitary. Specifically, it takes the form $\sim n^{4V}$ with $V$ the maximum volume of a past light cone in a circuit implementing the unitary. Thus we can implement unitary circuits with $V\sim O(1)$ using polynomial entanglement, and those with $V\sim \mathrm{polylog}(n)$ using quasi-polynomial entanglement. For a general unitary circuit with $d$ layers of $k$-qubit gates $V$ is at most $k^d$, but if geometric locality is imposed it is at most polynomial in $d$. We give an explicit class of unitaries for which our protocol's entanglement cost scales better than any known protocol. We also show that several extensions can be made without significantly affecting the entanglement cost - arbitrary local pre- and post-processing; global Clifford pre- and post-processing; and the addition of a polynomial number of auxiliary systems.
