arXiv 1704.034312017-04quant-ph

基于$χ^{(2)}$相互作用的Qudit基泛量子计算

Qudit-Basis Universal Quantum Computation using $χ^{(2)}$ Interactions

Murphy Yuezhen Niu, Isaac L. Chuang, Jeffrey H. Shapiro

备注：: 9 pages, 3 figures
发表信息：: Phys. Rev. Lett. 120, 160502 (2018)
DOI：: 10.1103/PhysRevLett.120.160502

摘要：

我们证明了在$n$ -泵浦光子子空间的任意$(n+1)$维量子基中，仅用线性光学和$χ^{(2)}$（三波混频）相互作用就可以实现普适量子计算.首先，我们展示了一个严格的通用门设置的量子比特基的单泵浦光子子空间。接下来，我们证明了qutri基的普适性，证明$χ^{(2)}$哈密顿算子和光子数算子在双泵浦光子子空间中生成完整的$\mathfrak{u}(3)$李代数，并展示了qutri控制的$Z$门如何仅用线性光学和$χ^{(2)}$相互作用来实现。然后，我们使用归纳证明，以获得我们的一般qudit结果。我们的归纳证明依赖于相干光子注入/减法，一种由编码模式和辅助模式之间的$χ^{(2)}$相互作用实现的技术。最后，我们表明相干光子注入不仅仅是一个概念性的工具，因为它提供了一条从单光子Fock态制备高光子数Fock态的途径。

英文摘要：

We prove that universal quantum computation can be realized---using only linear optics and $χ^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that $χ^{(2)}$ Hamiltonians and photon-number operators generate the full $\mathfrak{u}(3)$ Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-$Z$ gate can be implemented with only linear optics and $χ^{(2)}$ interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection/subtraction, a technique enabled by $χ^{(2)}$ interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.

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