Rome was not built in a day, neither would a general-purpose quantum computer. The groundwork has been laid in the past decade or so to achieve the remarkable progress in quantum algorithms and quantum computing. From NISQ-friendly variational hybrid quantum-classical algorithms, the design and implementation of quantum error correcting codes and error mitigation protocols, to demonstrable quantum advantages from optical and superconducting quantum chips, the road to practical quantum algorithms is filled with promising ideas. This session is dedicated to quantum algorithms: from the theoretical groundwork including variational quantum circuits and algorithms for quantum simulation and quantum chemistry, error mitigation and correction protocols, quantum complexity theory, to physical realizations of quantum algorithms and circuit with qubits made of photons, superconducting junctions, trapped ions or Rydberg atoms. We hope theorists propose experimental protocols suitable for the unique capabilities of each platform, while experimentalists can discover the latest theoretical proposals which will push the boundary of what can be done in their labs.