Qubit lattice representation of PT-symmetric BEC subsystems

PT invariant non-Hermitian Hamiltonians have become an important class of problems that permit a wider family of solutions than their more familiar Hermitian counterparts. In particular dark or bright solitons in the Hermitian Nonlinear Schrodinger equation require either a defocusing or focusing potential. However in the fully integrable PT non-Hermitian form it was shown that both dark and bright solitons can coexist simultaneously. Here we consider a qubit unitary representation of an open double-well BEC interacting subsystem whose evolution is given by non-Hermitian PT Hamiltonians [Wunner]. Under the usual Dirac inner product, this double-well system is non-unitary. These subsytems can be embedded into a higher-dimensional closed Hermitian system [Wunner] or used to perturbatively generate a Hermitian analog [Baraenskov]. A qubit unitary representation, with two qubits/lattice site for each scalar field, can now be generated. This give rise to an extremely parallelized algorithm that is not only ideal on classical supercomputers but readily coded onto a quantum computer because of its inherent unitarity. Quantum turbulence in such open PT-BEC systems is considered.