Correlated electron interferometers for quantum computing

Single-electron and two-electron interference have been realized in a large variety of devices operating in the Integer quantum Hall regime, making them possible candidates for a flying-qubit implementation of quantum computing architectures[3]. In Ref.[1], we demonstrated the viability of coherent electron transport in a scalable design of the Mach-Zehnder interferometer and proposed its integration in a Conditional Phase Shifter, a two-qubit logic gate able to perform the entangling transformation for a universal set of quantum gates. To this aim, we numerically setup the 2D potential landscape reproducing modulation gates on top of an Hall Conditional Phase Shifter at bulk filling factor 2, and investigate two-electron scattering driven by Coulomb repulsion in its active region. The dynamics of quasiparticles injected by single-electron sources in Hall interferometers is reproduced by describing charge carriers with localized wavepackets of edge states, and the exact two-fermion wavefunction is evolved with a parallel version of the Split-Step Fourier method[2]. In this approach, electron-electron interaction is introduced exactly in the two-particle Hamiltonian with a long-range Coulomb potential in 2D. We measure the spatial shift induced by Coulomb repulsion in the final two-electron wavefunction, and prove that electron-electron interaction generates a consistent phase shift in one of the four configurations of possible Landau levels occupancy at bulk filling factor 2. We further demonstrate that the conditional phase can be, in our design, as large as π and that it can be controlled by the static confinement potential.