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Ancilla-driven quantum computation with twisted graph states

Anders, J. and Andersson, E. and Browne, D. E. and Kashefi, E. and Oi, D. K. L. (2012) Ancilla-driven quantum computation with twisted graph states. Theoretical Computer Science, 430. pp. 51-72. ISSN 0304-3975

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We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects of the quantum circuit (Deutsch, 1989 [1]) and the one-way model (Raussendorf and Briegel, 2001 [2]) to overcome some of the 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. We characterise all two-qubit interactions which couple any ancilla qubit with any memory qubit, while satisfying certain desirable conditions. We require these interactions to implement unitary, stepwise deterministic and universal evolution. Moreover, it should be possible to standardise the computation, that is, applying all global operations at the beginning. 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 (Danos et al., 2007 [8]). Furthermore, we present the notion of causal flow for twisted graph states, based on the stabiliser formalism, to characterise the determinism. Finally we demonstrate a 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. (c) 2012 Elsevier B.V. All rights reserved.