The quasi-analog formulation of duality computers

The quasi-analog formulation of duality computers is provided, inspired from the actual path integral understanding of the double-slit experiment and the inadequacies of the standard formulation of duality computers in explaining the experiment. In (analog) quantum mechanics, position and momentum are not typically discrete variables, but it is feasible to take the qubit (digital) approximation by selecting a set of approximately orthogonal states as computational basis for the qubits, such as Gaussian states with sufficient distances. The qubit approximation as an effective representation cannot be used for addressing the question of whether the computational system evolves unitarily without violating linearity, and fine-grained dynamics can respect linearity when effective dynamics do not. A general limiting procedure for determining qubit states regardless of effective unitarity violation is provided. The new formulation resolves the zero wavefunction paradox naturally out of the box and provides a method for detecting the unnormalized zero wavefunction. The resulting formulation of duality computers does not require additional postselection or non-unitary operators over unitary quantum mechanics and has realistic potentials to provide additional computational advantage over ordinary quantum computers.