  The practical construction of scalable quantum computer hardware capable of
executing non-trivial quantum algorithms will require the juxtaposition of
different types of quantum systems. We analyze a modular ion trap quantum
computer architecture with a hierarchy of interactions that can scale to very
large numbers of qubits. Local entangling quantum gates between qubit memories
within a single register are accomplished using natural interactions between
the qubits, and entanglement between separate registers is completed via a
probabilistic photonic interface between qubits in different registers, even
over large distances. We show that this architecture can be made
fault-tolerant, and demonstrate its viability for fault-tolerant execution of
modest size quantum circuits.
