Fast Stabiliser Simulation with Quadratic Form Expansions

Stabiliser circuits are an important class of quantum circuits that have long been known to be classically simulable, but which are also central to practical techniques for quantum error correction. Our paper describes a way to do ‘fast’ classical simulation of stabiliser circuits. We expect these techniques to be used to improve the simulation of error correction procedures, and other stabiliser circuits in which measurement outcomes will be systematically correlated. A further aspect of the work is that it provides a proof of the celebrated Gottesman-Knill theorem without relying on the indirect representation of stabiliser tableaus: we expect that this may be of interest in an educational setting.

Niel de Beaudrap, Steven Herbert

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