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arXiv · 1704.03431

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

Murphy Yuezhen Niu·Isaac L. Chuang·Jeffrey H. Shapiro
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Abstract

We prove that universal quantum computation can be realized---using only linear optics and $\chi^{(2)}$ (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 $\chi^{(2)}$ 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 $\chi^{(2)}$ 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 $\chi^{(2)}$ 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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Murphy Yuezhen Niu, Isaac L. Chuang, Jeffrey H. Shapiro. 2017-04-11. Qudit-Basis Universal Quantum Computation using $\chi^{(2)}$ Interactions. https://doi.org/10.1103/physrevlett.120.160502

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