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Universal quantum computation with unlabeled qubits

By S Severini


We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits) and two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a non-local phase-flip (for a fixed but arbitrary coefficient), form a universal set for quantum computation on n qubits. A quantum circuit, with n-qubits and based on this set, is then a product of unitaries whose factors are chosen from a pool of three. A quantum algorithm based on this set can be interpreted as a discrete diffusion of a quantum particle on a de Bruijn graph, with auxiliary modifications of the phases associated to the arcs

Topics: General Theoretical Physics
Year: 2006
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Provided by: CERN Document Server
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