A practical scheme for quantum computation with any two-qubit entangling gate
arXiv:quant-ph/0207072 · doi:10.1103/PhysRevLett.89.247902
Abstract
Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].
3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc/
References in corpus (4)
- Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
- Universal simulation of Hamiltonian dynamics for qudits
- Optimal simulation of two-qubit Hamiltonians using general local operations
- Optimal simulation of nonlocal Hamiltonians using local operations and classical communication
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