English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give a new algorithm for computing the robustness of magic - a measure ofthe utility of quantum states as a computational resource. Our work ismotivated by the magic state model of fault-tolerant quantum computation. Inthis model, all unitaries belong to the Clifford group. Non-Clifford operationsare effected by injecting non-stabiliser states, which are referred to as magicstates in this context. The robustness of magic measures the complexity ofsimulating such a circuit using a classical Monte Carlo algorithm. It isclosely related to the degree negativity that slows down Monte Carlosimulations through the infamous sign problem. Surprisingly, the robustness ofmagic is submultiplicative. This implies that the classical simulation overheadscales subexponentially with the number of injected magic states - better thana naive analysis would suggest. However, determining the robustness of n copiesof a magic state is difficult, as its definition involves a convex optimisationproblem in a 4^n-dimensional space. In this paper, we make use of inherentsymmetries to reduce the problem to n dimensions. The total run-time of ouralgorithm, while still exponential in n, is super-polynomially faster thanpreviously published methods. We provide a computer implementation and give therobustness of up to 10 copies of the most commonly used magic states. Guided bythe exact results, we find a finite hierarchy of approximate solutions whereeach level can be evaluated in polynomial time and yields rigorous upper boundsto the robustness. Technically, we use symmetries of the stabiliser polytope toconnect the robustness of magic to the geometry of a low-dimensional convexpolytope generated by certain signed quantum weight enumerators. As aby-product, we characterised the automorphism group of the stabiliser polytope,and, more generally, of projections onto complex projective 3-designs.

Robustness of Magic and Symmetries of the Stabiliser Polytope