Twisted Graph States for Ancilla-driven Universal Quantum Computation

We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects both of the quantum circuit [1] and the one-way model [2] 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. The underlying mathematical model is based on a new entanglement resource called twisted graph states generated from non-commuting operators, leading to a surprisingly powerful structure for parallel computation compared to graph states obtained from commuting generators. [3]. The ADQC model is formalised in an algebraic framework similar to the Measurement Calculus [4]. 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 and quantum circuit models directly into ADQC.