In a continuing effort to improve upon previous work, a research team at the Graduate School of Science, Osaka City University, has applied its recently developed Bayesian phase difference estimation quantum algorithm to perform full configuration interaction (full-CI) calculations of atoms and molecules without simulating the time evolution of the wave function conditional on an ancillary qubit. Superior to conventional methods in terms of parallel execution of quantum gates during quantum computing, this new algorithm is expected to be much easier to implement in actual quantum computers.