Distributed quantum computation based on small quantum registers

We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on a probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high-fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (similar to 5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic nonlocal coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion traps or nitrogen-vacancy centers. Our scheme capitalizes on an efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it onto a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme and also present an alternative approach to fault-tolerant preparation of Greenberger-Horne-Zeilinger states.