The resource theory of stabilizer quantum computation

By Victor Veitch, S. Mousavian, Daniel Gottesman, Joseph Emerson. 2013

592 citations recorded by the source corpus.

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant stabilizer computation. We introduce two quantitative measures—monotones—for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behavior.

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

View Paper: https://www.semanticscholar.org/paper/e089995b1d5212a59f8865ffa2ceedefc2d31dbb

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Many-Body Quantum Magic (2020, methodology): “The Gottesman–Knill theorem [2, 3] provides motivations for understanding the quantum computation advantages through the resource theory of magic [4], where the stabilizer polytope STAB is considered to be the set of free states, as speedups over classical computers require states outside STAB.”
Schur–Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations (2017, background): “state jSisuch that jhSj ij2 1 9d2 sn( ). Our theorem gives a new quantitative meaning to the sum-negativity, and thereby to the related mana, a monotone from the resource theory of stabilizer states [VMGE14] that has attracted increasing attention in the theory of fault-tolerant quantum computation.”
Quantum resource theories (2018, methodology): “The QRT of stabilizer quantum computation provides one such approach (Veitch et al., 2014).”