Contextuality supplies the ‘magic’ for quantum computation

By Mark Howard, Joel J. Wallman, Victor Veitch, Joseph Emerson. Nature, 2014

688 citations recorded by the source corpus.

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 remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via ‘magic state’ distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple ‘hidden variable’ model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.

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

View Paper: https://www.semanticscholar.org/paper/08ef8db26cedbfe5eb13310fe3b6985b7250b24e

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Citations in the corpus

Quantum resource theories (2018, neutral): “Any state having a negative discrete Wigner function can be used, in principle, to demonstrate contextuality in some family of stabilizer measurements (Howard et al., 2014).”
Schur–Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations (2017, background): “.e., x w (x) = 1, but it can be negative. This negativity plays an important role { e.g., it is an obstruction to ecient classical simulability [VFGE12,ME12] and witnesses the onset of contextuality [HWVE14]. In fact, pure stabilizer states are characterized by having a nonnegative Wigner function|t”
Wigner Function Negativity and Contextuality in Quantum Computation on Rebits (2014, background): “[16] have expanded on the previous results of Veitch et al.”
Qudits and High-Dimensional Quantum Computing (2020, methodology): “Recent research shows that we can have a speedup in a fault tolerant quantum computation mode using the quantum contextuality [72].”