Some ideas for quantum algorithms in real-space. Ground state preparation in first quantization, using the integral form of the Schrödinger equation and a known ground state energy. Gaussians approximate both the potential and the convolution kernel of the Green’s operator. Current ideas split into two variants: one iterates the fixed-point operator until it converges, and one uses the quantum singular value transformation (QSVT) to project onto the fixed-point subspace.