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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
|
Vol.14 No.7&8 May 2014 |
Classical simulation complexity of extended Clifford circuits
(pp0633-0648)
Richard
Jozsa and Marrten Van den Nest
doi:
https://doi.org/10.26421/QIC14.7-8-7
Abstracts:
Clifford gates are a winsome class of quantum operations combining
mathematical elegance with physical significance. The Gottesman-Knill
theorem asserts that Clifford computations can be classically
efficiently simulated but this is true only in a suitably restricted
setting. Here we consider Clifford computations with a variety of
additional ingredients: (a) strong vs. weak simulation, (b) inputs being
computational basis states vs. general product states, (c) adaptive vs.
non-adaptive choices of gates for circuits involving intermediate
measurements, (d) single line outputs vs. multi-line outputs. We
consider the classical simulation complexity of all combinations of
these ingredients and show that many are not classically efficiently
simulatable (subject to common complexity assumptions such as P not
equal to NP). Our results reveal a surprising proximity of classical to
quantum computing power viz. a class of classically simulatable quantum
circuits which yields universal quantum computation if extended by a
purely classical additional ingredient that does not extend the class of
quantum processes occurring.
Key words:
Classical simulation, Clifford circuits |
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