  We introduce a new paradigm for quantum computing called Ancilla-Driven
Quantum Computation (ADQC) combines aspects of the quantum circuit and the
one-way model to overcome challenging issues in building large-scale quantum
computers. Instead of directly manipulating each qubit to perform universal
quantum logic gates or measurements, ADQC uses a fixed two-qubit interaction to
couple the memory register of a quantum computer to an ancilla qubit. By
measuring the ancilla, the measurement-induced back-action on the system
performs the desired logical operations.
  By demanding that the ancilla-system qubit interaction should lead to unitary
and stepwise deterministic evolution, and that it should be possible to
standardise the computation, that is, applying all global operations at the
beginning, we are able to place conditions on the interactions that can be used
for ADQC. We prove there are only two such classes of interactions
characterised in terms of the non-local part of the interaction operator. This
leads to the definition of a new entanglement resource called twisted graph
states generated from non-commuting operators. The ADQC model is formalised in
an algebraic framework similar to the Measurement Calculus. Furthermore, we
present the notion of causal flow for twisted graph states, based on the
stabiliser formalism, to characterise the determinism. Finally we demonstrate
compositional embedding between ADQC and both the one-way and circuit models
which will allow us to transfer recently developed theory and toolkits of
measurement-based quantum computing directly into ADQC.
