We construct the exchange gate with small elementary gates on the space of qudits, which consist of three controlled shift gates and three ”reverse” gates. This is a natural extension of the qubit case. We also consider a similar subject on the Fock space, but in this case it is not clear what elementary gates are. We present some related problems.

This article concerns the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there are sufficiently many particles and the initial manyparticle state is any Gibbs equilibrium state for noninteracting fermions (with Slater determinants as a special example). Assuming a bounded two-p...

By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, synthetic gauge field is generated in the Fock space of system. At critical flux ground state undergoes quantum phase transition which analogous to Meissner-Abrikosov-vortex found type-II superconductors applied magnetic field. A second involving attractive interactions between bosons BJJ shown enhance sensitivi...