Contextuality as a resource for quantum computation

Short answer: Contextuality is a quantum feature that, in several theoretical models of computation with magic states, has been shown to be a necessary resource. A 2014 preprint links its onset to universal computation by magic state distillation, a 2015 Physical Review X paper extends this to rebits, and a 2017 Physical Review Letters paper extends it to qubits. These are theory results, not demonstrated machines.

Contextuality and magic states

The 2014 preprint on ar5iv starts from a basic question: what is the source of the power in quantum computing? Its authors say they prove an equivalence between the onset of contextuality and the possibility of universal quantum computation via magic state distillation. They describe magic state distillation as the leading model for experimentally realizing fault-tolerant quantum computation.

They also suggest a unifying paradigm for the resources of quantum information: nonlocality is a particular kind of contextuality, and nonlocality is already known to be a critical resource for advantages in quantum communication. They say the resource framework has applications such as characterizing trade-offs between theoretical and experimental schemes and bounding the overhead of classically simulating quantum algorithms.

Rebits and Wigner function negativity

The 2015 Physical Review X paper describes a universal scheme of quantum computation by state injection on rebits, which are states with real density matrices. For this scheme the authors establish contextuality and Wigner function negativity as computational resources, extending the 2014 results to two-level systems. They define a Wigner function suited to n rebits, prove a corresponding discrete Hudson's theorem, introduce contextuality witnesses for rebit states, and discuss the compatibility of their result with state-independent contextuality.

Qubits

The 2017 Physical Review Letters paper says state-independent contextuality poses an a priori obstruction to treating regular qubits. The authors establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits, and illustrate the result with a concrete scheme related to measurement-based quantum computation.

Limits

All three works are theoretical. Each result is about a specific model, namely computation with magic states or state injection, and the abstracts say "a large class" of schemes on qubits, not all schemes. None of the three works reports a built device that uses these results.

FAQ

Is contextuality required for all quantum computation?

The three works do not say so. They establish it as a necessary resource in specific models: magic state distillation, rebit state injection, and a large class of qubit schemes (2017 paper).

How does contextuality relate to nonlocality?

The 2014 preprint says nonlocality is a particular kind of contextuality, and that nonlocality is already known to be a critical resource for quantum communication advantages.

What is a rebit?

The 2015 Physical Review X paper uses the term for a two-level state with a real density matrix.

Does the result cover ordinary qubits?

The 2017 paper says it establishes contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits, and notes that state-independent contextuality posed an obstruction to this case.

Has any of this been built?

The three works are theoretical. None of them reports a deployed system.