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Abstract
We introduce a new paradigm for quantum computing called AncillaDriven Quantum Computation (ADQC) which combines aspects of the quantum circuit (Deutsch, 1989 [1]) and the oneway model (Raussendorf and Briegel, 2001 [2]) to overcome some of the challenging issues in building largescale quantum computers. Instead of directly manipulating each qubit to perform universal quantum logic gates or measurements, ADQC uses a fixed twoqubit interaction to couple the memory register of a quantum computer to an ancilla qubit. By measuring the ancilla, the measurementinduced backaction on the system performs the desired logical operations.
We characterise all twoqubit 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 nonlocal part of the interaction operator. This leads to the definition of a new entanglement resource called twisted graph states generated from noncommuting 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 oneway and circuit models which will allow us to transfer recently developed theory and toolkits of measurementbased quantum computing directly into ADQC.
We characterise all twoqubit 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 nonlocal part of the interaction operator. This leads to the definition of a new entanglement resource called twisted graph states generated from noncommuting 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 oneway and circuit models which will allow us to transfer recently developed theory and toolkits of measurementbased quantum computing directly into ADQC.
Original language  English 

Pages (fromto)  5172 
Number of pages  22 
Journal  Theoretical Computer Science 
Volume  430 
DOIs  
Publication status  Published  2012 
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Projects
 1 Finished

Measurement based quantum computing and it's relation to other quantum models
1/03/08 → 31/07/13
Project: Research