Quantum computers promise dramatic advantages over their classical counterparts, but the
source of the power in quantum computing has remained elusive. Here we prove a …

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 …

A central problem in quantum information is to determine the minimal physical resources
that are required for quantum computational speed-up and, in particular, for fault-tolerant …

We present a method for estimating the probabilities of outcomes of a quantum circuit using
Monte Carlo sampling techniques applied to a quasiprobability representation. Our estimate …

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-
negative Wigner function are stabilizer states. The Clifford group is identified as the set of …

We describe a universal scheme of quantum computation by state injection on rebits (states
with real density matrices). For this scheme, we establish contextuality and Wigner function …

A bstract For any state in a D-dimensional Hilbert space with a choice of basis, one can
define a discrete version of the Wigner function—a quasi-probability distribution which …

We give a new algorithm for computing the robustness of magic-a measure of the utility of
quantum states as a computational resource. Our work is motivated by the magic state …

This paper comprises a review of both the quasi-probability representations of infinite-
dimensional quantum theory (including the Wigner function) and the more recently defined …

We describe schemes of quantum computation with magic states on qubits for which
contextuality and negativity of the Wigner function are necessary resources possessed by …