How to simulate a quantum computer using negative probabilities
arXiv:0805.0029 · doi:10.1088/1751-8113/42/27/275304
Abstract
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1, and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate and assigning a negative statistical weight to the outcomes of sequences with an odd number of negative probability operations. The exponential speed-up of a quantum computer can then be evaluated in terms of the increase in the number of sequences needed to simulate a single operation of the quantum circuit.
11 pages, including one figure and one table. Full paper version for publication in Journal of Physics A. Clarifications of basic concepts and discussions of possible implications have been added
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