TBA
We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the most interesting case being that of qubits. For multiple qubits, we find that quantum computation by Clifford gates and Pauli measurements on magic states can be efficiently classically simulated if the quasiprobability distribution of the magic states is non-negative. This provides the so far missing qubit counterpart of the corresponding result [V. Veitch et al., New J. Phys. 14, 113011 (2012)] applying only to odd dimension. Our approach is more general than previous ones based on mixtures of stabilizer states. Namely, all mixtures of stabilizer states can be efficiently simulated, but for any number of qubits there also exist efficiently simulable states outside the stabilizer polytope. Further, our simulation method extends to negative quasiprobability distributions, where it provides amplitude estimation. The simulation cost is then proportional to a robustness measure squared. For all quantum states, this robustness is smaller than or equal to robustness of magic.
Joint work with Juani Bermejo-Vega, Emily Tyhurst, Cihan Okay, Michael Zurel.
Contextuality has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality—the possible local measurement outcomes cannot all be pre-assigned. We prove a generalisation of this result to the case when the local measured systems are qudits and discuss some important differences arising between the qubit and qudit case from a resource-theoretic perspective.
Joint work with Sam Roberts and Stephen Bartlett.
We start by introducing the notions of measurement scenario and empirical model, the basic ingredients of a general, sheaf-theoretic approach to non-locality and contextuality. We then focus on studying contextuality from the point of view of resource theory. We introduce natural operations that combine contextual systems and control their use as resources, including the kind of classical control of quantum systems required by measurement-based quantum computation (MBQC) schemes. We consider a quantitative measure of contextuality – the contextual fraction – which behaves as a monotone under these 'free' operations, and we relate it to quantifiable advantages afforded by access to contextual resources, including in non-local games and in a form of MBQC.
Joint work with Samson Abramsky, Shane Mansfield, and Martti Karvonen. Some more recent developments will be covered in Martti's talk.
