Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation

Abstract

We provide a scheme for efficient simulation of a broad class of quantum optics experiments. Our efficient simulation extends the continuous variable Gottesman-Knill theorem to a lage class of non-Gaussian mixed states, thereby identifying that these non-Gaussian states are not an enabling resource for exponential quantum speed-up. Our resuls also provide an operationally motivated interpretation of negativity as non-classicality. We apply our scheme to the case of noisy singlephoton-added-thermal-states to show that this class admits states with positive Wigner function but negative P -function that are not useful resource states for quantum computation.

The computational power of normalizer circuits over black-box groups

“…Aside from generalizations of Clifford circuits [1-3, 12-15, 51-57] (which includes normalizer circuits), many other classes of restricted quantum circuits have been studied in the literature. Some examples (by no means meant to be an exhaustive list) are nearestneighbor matchgate circuits [16][17][18][19][98][99][100][101][102], the one-clean qubit model [103][104][105][106][107][108][109][110], circuit models based on Gaussian or linear-optical operations [20][21][22][111][112][113][114], commuting circuits [24][25][26][27], low-entangling 4 circuits [116,117] , low-depth circuits [118,119], tree-like circuits [119][120][121][122][123], low-interference circuits [124,125] and a few others [126,127].…”

Characterization of phase-averaged coherent states

“…Recently, states with positive Wigner functions have become interesting for efficient classical simulation of a broad class of quantum optics experiments. In [13,14] a protocol for classical simulations using non-Gaussian states with positive Wigner function was presented (see also the more recent [15]). Note that the Wigner function in ( 14) is not Gaussian, a feature that becomes evident from the plot of the function that shows a dip at the origin of the phase space (see figure 3).…”