We discuss the implementation of quantum logic in a system of strongly interacting particles. The implementation is qubitless since ``logical qubits'' don't correspond to any physical two-state subsystems. 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 the current theory of quantum information processing to include systems with permanent strong coupling between the two-state subsystems.
@article{arxiv.quant-ph/0203059,
title = {Qubitless Quantum Logic},
author = {Richard B. Kassman and Gennady P. Berman and Vladimir I. Tsifrinovich and Gustavo V. Lopez},
journal= {arXiv preprint arXiv:quant-ph/0203059},
year = {2007}
}