Quantum arithmetics via computation with minimized external control: The half-adder

The while-you-wait computing paradigm combines elements of digital and analog quantum computation with the aim of minimizing the need of external control. In this architecture the computer is split into logic units, each continuously implementing a single recurring multigate operation via the unmodulated Hamiltonian evolution of a quantum many-body system. Here we use evolutionary algorithms to engineer such many-body dynamics, and develop logic units capable of continuously implementing a quantum half-adder in a time-independent four-qubit network, where qubits are coupled with either Ising or Heisenberg interactions. Our results provide a step for the development of larger modules for full quantum arithmetics.