TY  - JOUR
A1  - Mari, Andrea
A1  - Eisert, Jens
T1  - Positive wigner functions render classical simulation of quantum computation efficient
T2  - Physical review letters
N2  - We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.
Y1  - 2012
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/35460
SN  - 0031-9007
VL  - 109
IS  - 23
PB  - American Physical Society
CY  - College Park
ER  -