Fig. 2
Surface-plasmon-based SWAP1/2 gate comprised of nonlinear graphene nanoribbons. Nanoribbons are brought together so that the plasmonic modes couple to each other via a Coulomb interaction. For a separation dz between the ribbons, there is an interaction length \(L = L_{{\mathrm{SWAP}}^{1/2}}\) after which the plasmon has 50-50% probability of remaining in the same mode or having swapped across ribbons. Thus, when a single plasmon is input in each mode, |1〉1|1〉2, we find the output state with a one plasmon in each mode, |1〉1|1〉2, in which case the gate succeeds, or b both plasmons in one of the modes, |2〉1|0〉2 or |0〉1|2〉2, in which case the gate fails. When a separable single-qubit is input into each mode (|ϕ〉, |ψ〉), an entangled state is created, \(\left| \phi \right\rangle _1\left| \psi \right\rangle _2 \to \frac{1}{{\sqrt 2 }}\left( {\left| \phi \right\rangle _1\left| \psi \right\rangle _2 + \left| \psi \right\rangle _1\left| \phi \right\rangle _2} \right)\). In the absence of nonlinearity in the waveguide and assuming indistinguishable plasmons, the HOM effect forces the plasmons to exit the gate in the same output mode, meaning that the gate always fails for |1〉1|1〉2. However, driven by the Zeno effect, the strong nonlinearity of the graphene waveguides reduces the probability that two plasmons are found in the same nanoribbon and increases the success probability. c We describe the SWAP1/2 gate as a six-state system where U is the coupling between ribbons, while γ and γ(2) are the intrinsic damping and two-plasmon absorption rates, respectively
