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arXiv · 0805.0029

How to simulate a quantum computer using negative probabilities

Holger F. Hofmann
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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.

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Holger F. Hofmann. 2009-05-28. How to simulate a quantum computer using negative probabilities. https://doi.org/10.1088/1751-8113%2F42%2F27%2F275304

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