Negative quasi-probability as a resource for quantum computation

By Victor Veitch, C. Ferrie, David Gross, Joseph Emerson. 2012

197 citations recorded by the source corpus.

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 quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analogue of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/712bb2d4d499f8f94d7be585257dee62e8d8c5be

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Citations in the corpus

Contextuality supplies the ‘magic’ for quantum computation (2014, unknown): “The independence number of the exclusivity graph associated with Σ~r is α(Γ~r) = p3 for all A~r ∈ ASIM so that, relative to our construction, exactly the states ρ /∈ PSIM are those that exhibit contextuality.”
The resource theory of stabilizer quantum computation (2013, methodology): “This established, in conjunction with the results of [45], that generally the amount of magic that can be extracted from a magic state is not equal to the amount required to create it: the magic of creation does not equal the magic of distillation.”
Corrigendum: Negative quasi-probability as a resource for quantum computation (2012, background): “Hence, in this important paradigm, the question of which physical resources are required for universal fault-tolerant quantum computation reduces to the following: which non-stabilizer states are necessary and su cient to promote stabilizer computation to universal quantum computation? In this talk ”
Simulation of quantum circuits by low-rank stabilizer decompositions (2018, methodology): “A similar class of simulation methods uses Monte Carlo sampling over quasiprobability distributions, where the distribution can be over either a discrete phase space [20, 47, 56], over the class of stabilizer states [32] or over stabilizer operations [7].”