Quasideterministic realization of a universal quantum gate in a single scattering process

We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-$\frac{1}{2}$ centers, such as quantum dots, can implement a controlled-z gate (universal for quantum computation) between them. This occurs quasideterministically in a single scattering event, with no need for any postselection or iteration and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.

Figure 1

Scheme working principle. (a) $f$ impinges on a set of SCs in $\rho$. (b) After the interaction, $f$ is either reflected or transmitted while the SCs undergo a nonunitary quantum map. (c) With a perfect mirror beyond the centers, $f$ can be only back reflected and the unitary $\widehat{R}$ is applied to the SCs.

Figure 2

Setups implementing our scheme. (a) An electron along a quantum wire with double quantum dots (DQDs). (b) A photon along a waveguide with $\Lambda$-type atomlike systems. The right end of the wire or waveguide behaves as a perfect mirror.