Twisted Graph States for Ancilla-driven Universal Quantum Computation

  • Authors:

  • E. Kashefi;D. K. L. Oi;D. Browne;J. Anders;E. Andersson

  • Affiliations:

  • School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, UK;SUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK;Department of Physics & Astronomy, University College London, London WC1E 6BT, UK;Department of Physics & Astronomy, University College London, London WC1E 6BT, UK;SUPA, Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

We introduce a new paradigm for quantum computing called Ancilla-Driven Quantum Computation (ADQC) which combines aspects both of the quantum circuit [D. Deutsch. Quantum computational networks. Proc. Roy. Soc. Lond A, 425, 1989] and the one-way model [R. Raussendorf and H. J. Briegel. A one-way quantum computer. Physical Review Letters, 86, 2001] 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. [M. Hein, J. Eisert, and H.J. Briegel. Multi-party entanglement in graph states. Physical Review A, 69, 2004. quant-ph/0307130]. The ADQC model is formalised in an algebraic framework similar to the Measurement Calculus [V. Danos, E. Kashefi, and P. Panangaden. The measurement calculus. Journal of ACM, 2007]. 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.