Quantum contextuality beyond the Pauli group as a resource of quantum computing

There is a string of recent papers that show that quantum contextuality is necessary for the quantum computation advantage.

The notion of quantum contextuality expresses that quantum mechanics is in conflict with classical models in which the outcome of a measurement does not depend on which other compatible measurements are jointly performed.

A simple form of quantum contextuality is available through qubit operations in the Pauli group, and it was recenty shown that Pauli group contextuality is needed for one specific quantum algorithm known as the Shallow circuits algorithm.

Somewhat surprisingly, a result from our group from 2022 is that the necessary Pauli group contextuality can be classically simulated at quadratic cost in memory and time.

Thus, to clarify the issue, this project intends to study how quantum contextuality beyond the Pauli group provides the advantage of quantum computing. The project plan is adapted to provide a PhD dissertation project, from start to finish.

We intend to build on the Shallow circuits quantum algorithm, but also study other explicit quantum algorithms and specific single gates that enable universal computing.

A better understanding of how quantum contextuality beyond the Pauli group enables the quantum computing advantage will aid future quantum engineers.

This will point to what parts of a quantum computer are especially demanding to realize, perhaps to the point of enabling the construction of large-scale quantum computers.