Qubitless Quantum Logic

AbstractWe discuss the implementation of quantum logic in a system of strongly interacting particles. The implementation is qubitless since “logical qubits” do not correspond to any well-defined physical substates. As an illustration, we present the results of simulations of the quantum controlled-NOT gate and Shor's algorithm for a chain of spin-1/2 particles with Heisenberg coupling. Our proposal extends quantum information processing theory to systems with permanent strong coupling between the two-state subsystems. PACS: 03.67.Lx; 03.65.Ta