  The scalability, error correction and practical problem solving are important
challenges for quantum computing (QC) as more emphasized by quantum supremacy
(QS) experiments. Quantum path computing (QPC), recently introduced for linear
optic based QCs (LOQCs) as an unconventional design, targets to obtain
scalability and practical problem solving. It samples the intensity from the
interference of exponentially increasing number of propagation paths obtained
in multi-plane diffraction (MPD) of classical particle sources. QPC exploits
MPD based quantum temporal correlations of the paths and freely entangled
projections a<t different time instants, for the first time, with the classical
light source and intensity measurement while not requiring photon interactions
or single photon sources and receivers. In this article, photonic QPC is
defined, theoretically modeled and numerically analyzed for arbitrary Fourier
optical or quadratic phase set-ups while utilizing both Gaussian and
Hermite-Gaussian source laser modes. Problem solving capabilities already
including partial sum of Riemann theta functions are extended. Important future
applications, implementation challenges and open issues such as universal
computation and quantum circuit implementations determining the scope of QC
capabilities are discussed. The applications include QS experiments reaching
more than $2^{100}$ Feynman paths, quantum neuron implementations and solutions
of nonlinear Schr\"odinger equation.
